名校
1 . 在数学中,由
个数
排列成的m行n列的数表
称为
矩阵,其中
称为矩阵A的第i行第j列的元素.矩阵乘法是指对于两个矩阵A和B,如果4的列数等于B的行数,则可以把A和B相乘,具体来说:若
,
,则
,其中
.已知
,函数
.
(1)讨论
的单调性;
(2)若
是
的两个极值点,证明:
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e70354d6ca5ad9f6b4592fac0b5e559.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db452ec3c9e60109fdfe9fae8e456edf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fc970ba32a45946c514e98eac1e80ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e70354d6ca5ad9f6b4592fac0b5e559.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37a14c188b1c9d61aa237b137ba18023.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16a9a7e6a7ff34bb72659677929bf9c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7cf279527982a84842a2d6a4f212892.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b65887e38142a10f30be2296310d1a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9408afcaa76f52987ca43733b828f66a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01f44187cd898fb01a4f8fa76bdc6cdd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b8d8e4e3f777270997845f7d9cfe85f.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aca579894dad67bc82cb715fd48e0d70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b3db0fe99d90b9a693562dd988eca5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/def4d3923ea803696106f42140e83bf4.png)
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3卷引用:山东省泰安市2024届高三四轮检测数学试题
山东省泰安市2024届高三四轮检测数学试题江西省宜春市宜丰中学2023-2024学年高二下学期6月月考数学试题(已下线)高二数学期末模拟试卷01【好题汇编】-备战2023-2024学年高二数学下学期期末真题分类汇编(北师大版2019选择性必修第二册)
名校
2 . 某投资公司现从甲投资研究室(
人)、乙投资研究室(
人)中随机选出
名资深投资顾问对某项目进行考察投资.
(1)记选出的
名资深投资顾问中,甲投资研究室的人数为
,求
的分布列和均值;
(2)为给投资提供决策依据,资深投资顾问对此项目的
个子项目调查了年研发经费
(单位:万元)和年销售额
(单位:十万元),并对数据进行了初步处理,得到一些统计量的值:
,
,
,
,根据散点图认为
关于
的经验回归方程为
,求
与
的值(结果精确到
).
参考公式:
,其中
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91e07104b699c4012be2d26160976a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
(1)记选出的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
(2)为给投资提供决策依据,资深投资顾问对此项目的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d07ae0b4264da6a8812454ffd2f20d94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97ea8f47d8d8d9e1832d52b1c7425450.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4de122ae929b1acaff321dec137622ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7756f25833e524da5a57715ef312186.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/713be36305fc8a06011cddeb34a05ed9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c36d445455548fa9c9265e92f6692ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05d542a22a43aa972991aef5881c773f.png)
![](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/1db6103cb0f1d2bd6b19235d53ee7e98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0032ca31e3cba58f973c6e75b907fb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abc5505526d11946ca7d3a4421a9e08f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a87796ee30e6c5d5e6b6285b32abe10c.png)
参考公式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a58291bd91befe1061530246da983727.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2dbdbf02e0dd324daba7488c3e3bf31.png)
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2卷引用:2024届山东省泰安肥城市高考仿真模拟(一)数学试题
解题方法
3 . 已知数列
是斐波那契数列,其数值为:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a4fb1a2d1cb1152ef78d7332d45b681.png)
.这一数列以如下递推的方法定义:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/642c7410a3134bed37df637e8d382c88.png)
.数列
对于确定的正整数
,若存在正整数
使得
成立,则称数列
为“
阶可分拆数列”.
(1)已知数列
满足![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c9e8b08ba803f851cf12404e742775.png)
.判断是否对
,总存在确定的正整数
,使得数列
为“
阶可分拆数列”,并说明理由.
(2)设数列
的前
项和为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75541174a021adfd2e3356ca2ad56f7b.png)
,
(i)若数列
为“
阶可分拆数列”,求出符合条件的实数
的值;
(ii)在(i)问的前提下,若数列
满足
,
,其前
项和为
.证明:当
且
时,
成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a4fb1a2d1cb1152ef78d7332d45b681.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc50612eece655796b752da6b4bc3f3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/642c7410a3134bed37df637e8d382c88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d74fa7fa6330976d7eb8e523a62cd09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.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/7cdfd9c3f8933cddb63d87dbe2812994.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(1)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5ab0309e2cd35585ea9fb2cc3017abf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c9e8b08ba803f851cf12404e742775.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/753358ca020523f27725f5187bb8e988.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/136a003907c455bfd58875c96c138772.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5ab0309e2cd35585ea9fb2cc3017abf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d813f3ca8db41a4db6c18eac30fef98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75541174a021adfd2e3356ca2ad56f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79282bbe9f6408297d6378878c423bec.png)
(i)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d813f3ca8db41a4db6c18eac30fef98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(ii)在(i)问的前提下,若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca5f894d605847c6df0c4df24cf8e1fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69a340cb0e3c456ec64ffdf89d7cd6ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09881de0dc186bbcd1e60eb00159ee97.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/09881de0dc186bbcd1e60eb00159ee97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e48268fd6d3f92032eb54fbf65c01405.png)
您最近一年使用:0次
解题方法
4 . 已知函数
是
上的奇函数,且过点
,对于一切正实数
,都有
. 当
时,
恒成立,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0d54423c3e960b9ce8e9303f4a4ad3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280860dd039e1305a5ccc455f63e8223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff44456e5e1d5cc91392aa3901e0ae3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53e036700c90418869c4880f676c207a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/018857ec6e498113b3b12a730d9313da.png)
A.![]() |
B.![]() ![]() |
C.![]() |
D.当![]() ![]() |
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解题方法
5 . 平面内点
到点
与到直线
的距离之比为3.
(1)求点
的轨迹
的方程;
(2)
为
的左右顶点,过
的直线
与
交于
(异于
)两点,
与
交点为
,求证:点
在定直线上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2254f7a85430f9c0b1adf193318dbf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82daff095e3184c8e4f42b0f547d6e3d.png)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00442d96d695db2c58bf1fb7165fca94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00442d96d695db2c58bf1fb7165fca94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbe61d39d080872caa8973a70a3b4955.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a439c8a01a6626d7a3f53af31ef0bcae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
您最近一年使用:0次
6 . 下列结论正确的是( )
A.回归直线![]() ![]() |
B.已知命题![]() ![]() ![]() ![]() ![]() |
C.若![]() ![]() |
D.若一组样本数据![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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7 . 圆台内有一个球,该球与圆台的侧面和上下底面均相切,球的球心为
.已知圆台上底面圆的半径为1,下底面圆的半径为
,母线与底面所成的角为
,且
.若该圆台的上下两个底面都在同一个球的球面上,该球的球心为
,记圆台的表面积为
,体积为
,球
的表面积为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad83973d1361b2928c7e783ffd073b75.png)
______ ,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90a3587375b61aba9c85c469e40f5148.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acd15bcd2eda1d7a943170b39a94a54a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da19f0d43a33b280c90491d999ce8227.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12fe32dfbd66709875c5b9f79c9496da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be54e84508decfcce6d2fcbe6c8c1a92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12fe32dfbd66709875c5b9f79c9496da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/150a135bbd528daf3f19a58a621a57c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad83973d1361b2928c7e783ffd073b75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90a3587375b61aba9c85c469e40f5148.png)
您最近一年使用:0次
解题方法
8 . 已知复数
的共轭复数为
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fcfebd9f5a57036e6df6b6e14865da3.png)
A.![]() |
B.若方程![]() ![]() ![]() |
C.满足![]() ![]() ![]() |
D.若![]() ![]() |
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名校
解题方法
9 . 利用方程的方法可以将无限循环小数化为分数,例如将
化为分数是这样计算的:设
,则
,即
,解得
.
这是一种利用方程求解具有无限过程的问题的方法,这种方法在高中计算无限概率、无限期望问题时都有很好的妙用.
已知甲、乙两人进行乒乓球比赛,每局比赛甲获胜的概率为
,乙获胜的概率为
,每局比赛的结果互不影响.规定:净胜
局指的是一方比另一方多胜
局.
(1)如果约定先获得净胜两局者获胜,求恰好4局结束比赛的概率;
(2)如果约定先获得净胜三局者获胜,那么在比赛过程中,甲可能净胜
局.设甲在净胜
局时,继续比赛甲获胜的概率为
,比赛结束(甲、乙有一方先净胜三局)时需进行的局数为
,期望为
.
①求甲获胜的概率
;
②求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f522d1f7a4158bbb09355fcf2ebe1748.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd96b78172b97a5fb995bc4fe7a91312.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c9a257d22b01103a676795f6a6b399e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8567750e1eb0471c3942c1456cdf2299.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0fae7b60887e1ae9ff3f6b2b959762e.png)
这是一种利用方程求解具有无限过程的问题的方法,这种方法在高中计算无限概率、无限期望问题时都有很好的妙用.
已知甲、乙两人进行乒乓球比赛,每局比赛甲获胜的概率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf31876698721a199c7c53c6b320aa86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(1)如果约定先获得净胜两局者获胜,求恰好4局结束比赛的概率;
(2)如果约定先获得净胜三局者获胜,那么在比赛过程中,甲可能净胜
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68061f9674fb257c62da194bebd65289.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59c709117ab1d3ef620883a732aed68b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f95e54a9b7c66c97dc6ee6161a25c0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56b678dec65a0ca8006cc6828d8cb501.png)
①求甲获胜的概率
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf9f50605db5d5f8f3a01ee8e474a112.png)
②求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fc8a872d7b16187634e8db2571c8cbe.png)
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2024-06-09更新
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1283次组卷
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2卷引用:山东省泰安第一中学2023-2024学年高二下学期5月月考数学试题
解题方法
10 . 增强青少年体质,促进青少年健康成长,是关系国家和民族未来的大事.某高中为了解本校高一年级学生体育锻炼情况,随机抽取体育锻炼时间在
(单位:分钟)的50名学生,统计他们每天体育锻炼的时间作为样本并绘制成如下的频率分布直方图,已知样本中体育锻炼时间在
的有5名学生.
(2)若从样本中体育锻炼时间在
的学生中随机抽取4人,设X表示在
的人数,求X的分布列和均值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/318354c17e916f02f5f6fa90d7a2b347.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea146d8ec45e63ad14683fd31064de66.png)
(2)若从样本中体育锻炼时间在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efa08c19f47274f4fa0e1b6672561b52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b07d0044910af65bd57004a28379152d.png)
您最近一年使用:0次