名校
解题方法
1 . 用一个内底面直径为3,高为20的圆柱体塑料桶去装直径为2的小球,最多能装下小球个数为( )
A.10 | B.11 | C.12 | D.13 |
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2卷引用:浙江省浙南名校联盟2023-2024学年高一下学期4月期中联考数学试题
解题方法
2 . 已知
的数列
满足
,
,
成公差为1的等差数列,且满足
,
,
成公比为
的等比数列;
的数列
满足
,
,
成公比为
的等比数列,且满足
,
,
成公差为1的等差数列.
(1)求
,
.
(2)证明:当
时,
.
(3)是否存在实数
,使得对任意
,
?若存在,求出所有的
;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/111d1a60e77d0293acdc3ea1c647d892.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29a7054cf2f1fefdcea1bb11d966cd8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f339d05a6032c0ca8c4187e75d8ae156.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f339d05a6032c0ca8c4187e75d8ae156.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73c0a2ab7198ec8e80904285ca6eb762.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cbbadf02a2855e91a86dedc7a98781a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59dd6c97d2ee3e74ba5730f1cbcc1d43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/306f3c49c9e05cfafadff14fdf90c3f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/965e8beb4ffed1c9cb0110b7e3f580f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8f51bf9165826c40663d01427c24aba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8f51bf9165826c40663d01427c24aba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56c0ec55d00d28d1a877e6ea38d6cd69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e3875830b3121133833a3b45d3407b6.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f65fc200f10b97588a0c9896277c9c64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f6714682274c31a328bf796e235900.png)
(2)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c881b38e5e74dba689507bde6dfa3c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e87d6c4b41cede82adf564ecb513f326.png)
(3)是否存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/209559aca6bf32705588b6a40e0b7320.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63b6c614a413bd1db7b6de3a8ff7e7d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
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3 . 半正多面体是由两种或两种以上的正多边形围成的多面体.半正多面体体现了数学的对称美.如图在一个棱长为4的正方体中,
,
,……,
,过
三点可做一截面,类似地,可做8个形状完全相同的截面.关于截面之间的位于正方体正中间的这个几何体,下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d36fb8219ce5186e7bb59a132eb881ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3ff01e2d34ecd3a793aefca53539ba1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05700c3d8a6eddac23d7ff80dcccccc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2e2fff17f81d5d24e3c76039b7ed51b.png)
A.当此半正多面体是由正八边形与正三角形围成时,边长为2 |
B.当此半正多面体是由正方形与正三角形围成时,表面积是![]() |
C.当此几何体为半正多面体时![]() ![]() |
D.当此几何体是半正多面体时,可能由正方形与正六边形围成 |
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解题方法
4 . 已知点
为焦点在
轴上的等轴双曲线上的一点.
(1)求双曲线的方程;
(2)已知直线
且
交双曲线右支于
两点,直线
分别交该双曲线斜率为正的渐近线于
两点,设四边形
和三角形
的面积分别为
和
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f40d5459e1385ab7d829ea96ca0b946.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(1)求双曲线的方程;
(2)已知直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/108cab3ffbf5705366ad2f3af6bb9e09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ec8858389f4c3156a946ba8bf0d8a7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12f4248e8021130ab60365e3d2e9a694.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d246f9eceab371ebf47a47c2f11a4ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/235f0a6fb218d28383e6f27f2df1f50f.png)
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解题方法
5 . 在高等数学中对于二阶线性递推式
求数列通项,有一个特殊的方法特征根法:我们把递推数列
的特征方程写为
①,若①有两个不同实数根
,则可令
;若①有两个相同的实根
,则可令
,再根据
求出
,代入即可求出数列
的通项.
(1)斐波那契数列(Fibonacci sequence),又称黄金分割数列,因出自于意大利数学家斐波那契的一道兔子繁殖问题而得名.斐波那契数列指的是形如
的数列,这个数列的前两项为1,从第三项开始,每一项都等于前两项之和,请求出斐波那契数列的通项公式;
(2)已知数列
中
,数列
满足
,数列
满足
,求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c48a2440b4b2c3723ad87edfc8193c68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c48a2440b4b2c3723ad87edfc8193c68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/594d0e29aa2515d2eba9a5ddafd144f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4e288596fa3811dd2c17bded60e82e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3490528838590538ce9b50f4ae6885e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91bd27ae250b40955a3c30e60095b6ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0158862238e250d2a2598b7d4ecd148.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/595978a4c58acd102b120735f963a631.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)斐波那契数列(Fibonacci sequence),又称黄金分割数列,因出自于意大利数学家斐波那契的一道兔子繁殖问题而得名.斐波那契数列指的是形如
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72a59cc32eebe1accdf2fa8ba0aa916d.png)
(2)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db1be42847d98a18aeffba68d2dbd8de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97a8e8e16b1adc46119e77d74b7ed519.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65146e1a9e8192e773871cad3cc48d89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
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6 . 已知函数
(
是自然对数的底数),则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c715d433b58fea1e74049279cbbd17f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a82d68ed3c2ae422e6b0a312f0bf5523.png)
A.若![]() ![]() ![]() |
B.若![]() ![]() ![]() |
C.若![]() ![]() ![]() |
D.当![]() ![]() ![]() ![]() |
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7 . 设非空数集M,对于M中的任意两个元素,如果满足:①两个元素之和属于M ②两个元素之差属于M.③两个元素之积属于M ④两个元素之商(分母不为零)也属于M.定义:满足条件①②③的数集M为数环(即数环对于加、减、乘运算封闭);满足④的数环M为数域(即数域对于加、减、乘、除运算封闭).
(1)判断自然数集N、整数集Z、有理数集Q、实数集R、复数集C是不是数环,假如该集合是数环,那么它是不是数域(无需说明理由);
(2)若M是一个数环,证明:
;若S是一个数域,证明:
;
(3)设
,证明A是数域.
(1)判断自然数集N、整数集Z、有理数集Q、实数集R、复数集C是不是数环,假如该集合是数环,那么它是不是数域(无需说明理由);
(2)若M是一个数环,证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca05074e5a317ae45d073962bdf74dbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81b48f8ebf391353fdd01dbf0670df8.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ad037818426ec563f10cb69ccb4a4a6.png)
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8 . 二阶递推公式特征方程是一种常见的数学方法,主要用于求解二阶线性递推数列的通项公式.例如:一个数列满足递推关系
,且
,
为给定的常数(有时也可以是
,
为给定的常数),特征方程就是将上述的递推关系转化为关于
的二次特征方程:
,若
,
是特征方程的两个不同实根,我们就可以求出数列的通项公式
,其中
和
是两个常数,可以由给定的
,
(有时也可以是
,
)求出.
(1)若数列
满足:
,
,
,求数列
的通项公式
;
(2)若
,试求
的十分位数码(即小数点后第一位数字),并说明理由;
(3)若定义域和值域均为
的函数
满足:
,求
的解析式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c48a2440b4b2c3723ad87edfc8193c68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f35f7dcce39f3d4dc6b7faf84dc1d0a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/594d0e29aa2515d2eba9a5ddafd144f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4c6c3692be3b17d33bc3770a747a01a.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/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f35f7dcce39f3d4dc6b7faf84dc1d0a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2693734765399876e9e93cdb110231c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a09a4bc955b154b3056aedfb5921640.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed21983b0e4303885c8a7b8a5283735e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f11075f2c574b6c59b97fb3038000e38.png)
(3)若定义域和值域均为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a682fef3ed23bfbf6a250fc2b61c14af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
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|
307次组卷
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4卷引用:浙江省五校联盟2023-2024学年高二下学期期中考试数学试卷
浙江省五校联盟2023-2024学年高二下学期期中考试数学试卷(已下线)模块三 专题3 高考新题型专练(专题2:新定义专练)(北师大)(高二)2024届海南省省直辖县级行政单位琼海市高考模拟预测数学试题广东省佛山市南海区桂城中学2023-2024学年高三下学期5月月考数学试题
名校
9 . 每年的 3 月 14 日是“国际圆周率日”,这是为纪念中国古代数学家祖冲之发现圆周率而设立的.2024 年 3月 14日,某班级为纪念这个日子,特举办数学题答题比赛. 已知赛题共 6道(各不相同),其中 3 道为高考题,另 3 道为竞赛题,参赛者依次不放回地从 6 道赛题中随机抽取一题进行作答,答对则继续,答错(或不答) 或者 6道题都答对即停止并记录答对题数.
(1)举办方进行模拟抽题,设第
次为首次抽到竞赛题,求
的分布列;
(2)
同学数学成绩优异,但没有参加过竞赛培训,高考题答对的概率为
,竞赛题答对的概率为
.
①求
同学停止答题时答对题数为1的概率;
②已知
同学停止答题时答对题数为2,求这两题抽到竞赛题题数
的均值.
(1)举办方进行模拟抽题,设第
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef9c407a9e79f3612690b9cff43a08e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8ee628efd6b2f7296c106dd5cbae42f.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
②已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a829fdd8ec0f3b7ede883cf2c3e53b.png)
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2卷引用:浙江省G5联盟2023-2024学年高二下学期4月期中联考数学试题
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10 . 已知某
的直角三角板斜边长
,动点P到直角顶点距离始终为
,记P到三角板斜边两个端点距离分别为
,则
范围为____________ (单位平方厘米).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6b86c22b670a8e9f3896f9e8883fbbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdb26c5cdef6f16f4b39cd091041b439.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc31bf4b6ed8cf336432a5a2791e67e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc5d70176873d0db587aef076102723c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c39ccc43fac44ef2f172209434ea7ec.png)
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