1 . 如图所示,点
为正方体形木料
上底面的动点,则下列结论正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
A.三棱锥![]() |
B.存在点![]() ![]() ![]() |
C.不存在点![]() ![]() ![]() |
D.经过点![]() ![]() ![]() ![]() ![]() ![]() |
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解题方法
2 . 如图所示,已知点
,
轴于点
,点
为线段
上的动点(
不与端点
重合),
轴于点
,
于点
,
与
相交于点
,记动点
的轨迹为
.
的方程;
(2)点
是
上不同的两点,
关于
轴对称的点为
,记直线
与
轴的交点为
,直线
与
轴的交点为
.当
为等边三角形,且
时,求点
到直线
的距离的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4fe7df5efe498440449d4c2b340df0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05b45db8dd8768994af51206565379fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ffc62c28c53286cd17e9eb997af7221.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcec4050ad922c18239c38effcc45403.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc0e7a1541a8db0c059fd6cd0c4c3620.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a299d2b999568e80be8005565ba209a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83042953e7f15e984b2da2ee9ca678d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b3265b7f882e7430dcfc27304bef3c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28b1ba4307cfde9b424d468bfcdf6c5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e91df8b5d2d51900151398baf13a15d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7463328ad1cffdd1a841aba1b2b3f7b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50b3ae183997b707d16eb4e7f6712fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07d824821175f4e0e7803cadf921e48e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9554c404e670a784d9a7e4df26ecd001.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
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3 . 宋朝诗人王镃在《蜻蜓》中写到:“轻绡剪翅约秋霜,点水低飞恋野塘”,描绘了蜻蜓点水的情形,蜻蜓点水会使平静的水面形成水波纹,截取其中一段水波纹,其形状可近似于用函数
的图象来描述,如图所示,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc4f29a473e9757d8f24f627f52e9e15.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3434f3860fb9e47ab2b8ef93eae2a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc4f29a473e9757d8f24f627f52e9e15.png)
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解题方法
4 . 某市开展“安全随我行”活动,交警部门在某个交通路口增设电子抓拍眼,并记录了某月该路口连续10日骑电动摩托车未佩戴头盔的人数
与天数
的情况,对统计得到的样本数据
作了初步处理,得到下面的散点图及一些统计量的值.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/6/19/0aaac424-3688-4c46-9668-42819e4498f9.png?resizew=165)
表中
,
.
(1)依据散点图推断,
与
哪一个更适合作为未佩戴头盔人数
与天数
的回归方程类型?(给出判断即可,不必说明理由)
(2)依据(1)的结果和上表中的数据求出
关于
的回归方程.
(3)为了解佩戴头盔情况与性别的关联性,交警对该路口骑电动摩托车市民进行调查,得到如下列联表:
依据
的独立性检验,能否认为市民骑电动摩托车佩戴头盔与性别有关联?
参考公式:
,
,
,其中
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46b4829b8c04f68d08b4272f1e5b7d0c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/6/19/0aaac424-3688-4c46-9668-42819e4498f9.png?resizew=165)
![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
5.5 | 8.7 | 1.9 | 301 | 385 | 79.75 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db7179f49001d08c5011a1dcbfdc7930.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4beaf3d206d85e2e6c8d25ab79b62e1c.png)
(1)依据散点图推断,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33b447ac3d1a965572c31b6e4c18d4b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56a9622a53d958999eecaefc85597b52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)依据(1)的结果和上表中的数据求出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(3)为了解佩戴头盔情况与性别的关联性,交警对该路口骑电动摩托车市民进行调查,得到如下列联表:
性别 | 佩戴头盔 | 合计 | |
不佩戴 | 佩戴 | ||
女性 | 8 | 12 | 20 |
男性 | 14 | 6 | 20 |
合计 | 22 | 18 | 40 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29f81f285940b14b97f368469121efab.png)
参考公式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07c226c805bf76bc0ad35c45806feb73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a58291bd91befe1061530246da983727.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b38cfee12dbeeab57c707dca8643538a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/356b05e46b10ee51c3e43546d73ec96c.png)
![]() | 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 |
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5 . 已知数列
,
,函数
,其中
,
均为实数.
(1)若
,
,
,
,
,
(ⅰ)求数列
的通项公式;
(ⅱ)设数列
的前
项和为
,求证:
.
(2)若
为奇函数,
,
,
且
,问:当
时,是否存在整数
,使得
成立.若存在,求出
的最大值;若不存在,请说明理由.(附:
,
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c2b44ac9ffc5dd71901d5cae704f059.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09881de0dc186bbcd1e60eb00159ee97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88f2599ca8b6b683e57a82699c8b1ebb.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b970d657304931a9d5cecdb044968f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a783088120d67cc98936081e80fb7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32003b56a60c9977c5d5d667c4136f62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/385275d29d8c8a7841eaeaa3dfab2cdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51b14938503c29201f32d30deda61db3.png)
(ⅰ)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
(ⅱ)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411bfe81694849b77de8b87f2651975a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43af3d8ebe0e5f0a905d42d29afe6f6f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66e442aaf3fda101960c18cc41de1614.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d39c60d4618060bbdc332282f0a0dd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f7cc67b3e263a2562be3c4c80dd5a5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bfb7ad7e6f4bbe0ec8dc3bec7d49025.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/570c49bcd783ed65a16b7bc565347094.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0e474d29ab7f3a4e404f593e90ae8b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10c1868215cf7dbeb9dd228d2cede3e9.png)
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6 . 已知椭圆
.
(1)已知
的顶点均在椭圆
上,若坐标原点
为
的重心,求点
到直线PQ距离的最小值;
(2)已知定
在椭圆
上,直线
(与
轴不重合)与椭圆交于A、B两点,若直线AB,AN,BN的斜率均存在,且
,证明:直线AB过定点(坐标用
,
表示).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/533b93dd6eb6b474481247736699c76c.png)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84a9dabb53dc826019fc8b6ae6d940c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84a9dabb53dc826019fc8b6ae6d940c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
(2)已知定
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/128aa322f3e76e8f03a7402bb2b2ae25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edf2fba59281e535ec54eed7fc2349bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8112f9185c7d48b015d9cd0525616b31.png)
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解题方法
7 . 下列说法正确的有( )
A.若角![]() ![]() ![]() ![]() |
B.若![]() ![]() |
C.若![]() ![]() |
D.若扇形的周长为![]() ![]() ![]() |
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名校
8 . 某校举办运动会,其中有一项为环形投球比寒,如图,学生在环形投掷区
内进行投球.规定球重心投掷到区域
内得3分,区域
内得2分,区域
内得1分,投掷到其他区域不得分.已知甲选手投掷一次得3分的概率为0.1,得2分的概率为
,不得分的概率为0.05,若甲选手连续投掷3次,得分大于7分的概率为0.002,且每次投掷相互独立,则甲选手投掷一次得1分的概率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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7日内更新
|
181次组卷
|
3卷引用:湖南省2024届高三下学期数学模拟试题
名校
解题方法
9 . 甲、乙、丙、丁、戊5名大学生实习时,有A,B,C三家企业可供选择,若去C企业最多一人,则不同分配种数是 ____________ .
您最近一年使用:0次
名校
解题方法
10 . 记
.
(1)若
,求
和
;
(2)若
,求证:对于任意
,都有
,且存在
,使得
.
(3)已知定义在
上
有最小值,求证“
是偶函数”的充要条件是“对于任意正实数
,均有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d80225e12934cd8d4ffc73d5fad815d.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04beea76c59a6c5b096d8c5a3b77f8a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e1b9f62690647a1597f4000ad5a64b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4c8381377b90826897eb4bf16cb3bae.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28034dcafe542a98d95d4504ad7d8a3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4def7108b0a2338f07a0143b00b48271.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3761d7ab4d00c91177fdbde67af36089.png)
(3)已知定义在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/625e9d3c298a595678933b59583632c2.png)
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