名校
解题方法
1 . 设抛物线C:
(
),直线l:
交C于A,B两点.过原点O作l的垂线,交直线
于点M.对任意
,直线AM,AB,BM的斜率成等差数列.
(1)求C的方程;
(2)若直线
,且
与C相切于点N,证明:
的面积不小于
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b35f0b940c8422ef47edc3b7ce55e47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5abd313d4e92a762fb7fb0c1cb65263d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02ebce8b2a915356ed39f36c5bad2ebe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1d0aa9412dd7caf42cc71520e282328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aff8d9b6533ff319420cdc5e8740b04.png)
(1)求C的方程;
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edc05c94ee6367e5551b219ac3168865.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13dea1bd3d0dd84b8b6f6ff634c5600c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98013a5042685a1db94249e70c62c09a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
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2024-05-26更新
|
3028次组卷
|
5卷引用:江西省南昌市八一中学2024届高三下学期三模测试数学试题
江西省南昌市八一中学2024届高三下学期三模测试数学试题2024届广东省深圳市二模数学试题(已下线)第30题 几何分析曲径通幽,代数推演水到渠成(优质好题一题多解)安徽省六安第一中学2023-2024学年高三下学期期末质量检测卷(二)数学试题(已下线)易错点8 圆锥曲线问题中未讨论直线斜率的特殊情况
解题方法
2 . 如图,有一张较大的矩形纸片
分别为AB,CD的中点,点
在
上,
.将矩形按图示方式折叠,使直线AB(被折起的部分)经过P点,记AB上与
点重合的点为
,折痕为
.过点
再折一条与BC平行的折痕
,并与折痕
交于点
,按上述方法多次折叠,
点的轨迹形成曲线
.曲线
在
点处的切线与AB交于点
,则
的面积的最小值为_________________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dcab46b9032d25a660af389a6a37210.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/192f4f9446c954a291f779d963f90257.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8d71ba52c97faad3a085b9989969145.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d36626c9e45a25e8dc5bf4be4dbbfb3.png)
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2024-05-20更新
|
710次组卷
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3卷引用:江西省南昌市2024届高三第二次模拟测试数学试题
3 . 如图所示,用一个不平行于圆柱底面的平面,截该圆柱所得的截面为椭圆面,得到的几何体称之为“斜截圆柱”.图一与图二是完全相同的“斜截圆柱”,AB是底面圆
的直径,
,椭圆所在平面垂直于平面ABCD,且与底面所成二面角为
,图一中,点
是椭圆上的动点,点
在底面上的投影为点
,图二中,椭圆上的点
在底面上的投影分别为
,且
均在直径AB的同一侧.
时,求
的长度;
(2)(i)当
时,若图二中,点
将半圆均分成7等份,求
;
(ii)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/526908dfb46cf151b8ab1492a9d52047.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30c20e88a33043f4279fff360c81006e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d1d663b6001346d11600f064cfcb7a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07d26ebb800066a7bce57213cd074005.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07d26ebb800066a7bce57213cd074005.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b20bf4f818b494e7b5fa9c68527026e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/893ff0f9b64c66312c37cb7ce90c351d.png)
(2)(i)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c345907ebe27888332b1b44c666cc47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bde134aa77da12366e6a742fa33b4bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e578d74f75cf5a087cb5dbad1d07c66.png)
(ii)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d0838e80d58bad3e9cbc4766d2a0ec3.png)
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解题方法
4 . 校足球社团为学校足球比赛设计了一个奖杯,如图,奖杯的设计思路是将侧棱长为6的正三棱锥
的三个侧面沿AB,BC,AC展开得到面
,使得平面
均与平面ABC垂直,再将球
放到上面使得
三个点在球
的表面上,若奖杯的总高度为
,且
,则球
的表面积为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66a3857b390b5cd3618625795b0cd4fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66a3857b390b5cd3618625795b0cd4fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f7807638578edd712265463a7a5eab0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ec978eb43bc4f9e7df83b0d0195dcda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
解题方法
5 . 已知
,则下列说法中正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80991f7aa65ba60e34ba031ea631acb0.png)
A.![]() ![]() |
B.若![]() ![]() ![]() |
C.![]() ![]() |
D.![]() |
您最近一年使用:0次
解题方法
6 . 为了解中学生喜爱足球运动与性别是否有关,甲、乙两校的课题组分别随机抽取了本校部分学生进行调查,得到如下两个表格:
).
则下列判断中正确的是( )
喜爱足球运动 | 不喜爱足球运动 | 合计 | |
男性 | 15 | 5 | 20 |
女性 | 8 | 12 | 20 |
合计 | 23 | 17 | 40 |
甲校样本
喜爱足球运动 | 不喜爱足球运动 | 合计 | |
男性 | 70 | 30 | 100 |
女性 | 45 | 55 | 100 |
合计 | 115 | 85 | 200 |
乙校样本
(参考公式及数据:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5faae3568e6ebcf20e57d05f14b9e25d.png)
0.1 | 0.01 | 0.001 | |
2.706 | 6.635 | 10.828 |
A.样本中,甲校男学生喜爱足球运动的比例高于乙校男学生喜爱足球运动的比例 |
B.样本中,甲校女学生喜爱足球运动的比例高于乙校女学生喜爱足球运动的比例 |
C.根据甲校样本有![]() |
D.根据乙校样本有![]() |
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7 . 一次知识竞赛中,共有
五个题,参赛人每次从中抽出一个题回答(抽后不放回). 已知参赛人甲A题答对的概率为
,B题答对的概率为
,
题答对的概率均为
,则甲前3个题全答对的概率为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1d75df9d80ce1e0b7cb50464e293864.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b2a698891d42c70b597f0da4f215f09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56d266a04f3dc7483eddbc26c5e487db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d14af8de7575341e02ee92cd0e33312b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
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解题方法
8 . 一条生产电阻的生产线,生产正常时,生产的电阻阻值
(单位:
)服从正态分布
.
(1)生产正常时,从这条生产线生产的电阻中抽取2只,求这两只电阻的阻值在区间
和
内各一只的概率;(精确到
)
(2)根据统计学的知识,从服从正态分布
的总体中抽取容量为
的样本,则这个样本的平均数服从正态分布
. 某时刻,质检员从生产线上抽取5只电阻,测得阻值分别为:1000,1007,1012,1013,1013(单位:Ω). 你认为这时生产线生产正常吗?说明理由.(参考数据:若
,则
,
,
.)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa35373ec4e4684107b42adb7a5161.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1819b5f181bc6de2db81a634f7c4d6a.png)
(1)生产正常时,从这条生产线生产的电阻中抽取2只,求这两只电阻的阻值在区间
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7d7de1142e14c514f3df9996e69b909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2fe05a165bcbdb749bfd3708a8ad413.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/042e234d538bc2c789d7c5a314f1ca92.png)
(2)根据统计学的知识,从服从正态分布
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29bcc248a7770a16fa10fc4602d71e0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5514a991619b0d9643ae4cadaa588ceb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1290917c2c835b61384480b335cc1d13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55084f692892749525ee229d1ff8027f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e1ca899fe3a9104666f7fb6c5310064.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047573288e225b5d060a4dbfb1dad35c.png)
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9 . 已知
,
为
上一点,且满足
. 动点
满足
,
为线段
上一点,满足
,则下列说法中正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08e39fda3cda5ddc03b085413f2030aa.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/c8f750b00c80522cbf882b082def2ae4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaea990fecc2f3d041f04e0350109545.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60873ab38fcd6afbdcd8c1416a528a13.png)
A.若![]() ![]() |
B.当![]() ![]() ![]() |
C.点![]() ![]() |
D.![]() ![]() |
您最近一年使用:0次
2024-04-29更新
|
470次组卷
|
2卷引用:江西省南昌市2024届高三第二次模拟测试数学试题
10 . 已知圆柱
的下底面在半球
的底面上,上底面圆周在半球
的球面上,记半球
的底面圆面积与圆柱
的侧面积分别为
,半球
与圆柱
的体积分别为
,则当
的值最小时,
的值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/192f4f9446c954a291f779d963f90257.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/192f4f9446c954a291f779d963f90257.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764097a1c5dd527fed0324ff4f352ee6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/192f4f9446c954a291f779d963f90257.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa389c037394797e7da193a8acfda2cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9dde419bc0440485e48b67644a2c078b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/669665c5abbdd7ff8f50ab23ded054bc.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2024-04-19更新
|
1079次组卷
|
3卷引用:江西省南昌市第十九中学2024届高三下学期第三次模拟考试数学试题