1 . 已知正方形
的边长为
,两个点
,
(两点不重合)都在直线
的同侧(但
,
与
在直线
的异侧),
,
关于直线
对称,若
,则
面积的取值范围是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/134c3d2c318a33a82da4134dd17fa57e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.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/10109d34ef06c3e721fd2c7128c5b9ca.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7393358bb94b0df78fd4e29223257e1.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/902f97913e1af1e6c793f7edfe6b2114.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6315136b2449842c9894529e25e3b445.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb9a99e6336047697901dd4a330ed634.png)
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4卷引用:福建省龙岩市上杭县第一中学2024届高三下学期5月数学模拟试题
2 . 灯笼起源于中国的西汉时期,两千多年来,每逢春节人们便会挂起象征美好团圆意义的红灯笼,营造一种喜庆的氛围.如图1,某球形灯笼的轮廓由三部分组成,上下两部分是两个相同的圆柱的侧面,中间是球面的一部分(除去两个球缺).如图2,“球缺”是指一个球被平面所截后剩下的部分,截得的圆面叫做球缺的底,垂直于截面的直径被截得的一段叫做球缺的高.已知球缺的体积公式为
,其中
是球的半径,
是球缺的高.已知该灯笼的高为40cm,圆柱的高为4 cm,圆柱的底面圆直径为24 cm,则该灯笼的体积为(取
)( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d752ac0180ffc7ba53d1aee0286c7948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eabd5f3a86afe49dcd70571e2b96cfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eb526a84a615236dc9484c873295eb8.png)
A.![]() | B.33664 cm3 | C.33792 cm3 | D.35456 cm3 |
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5卷引用:福建省龙岩市上杭县第一中学2024届高三下学期5月数学模拟试题
名校
解题方法
3 . 复数
是虚数单位
在复平面内对应点为
,设
是以
轴的非负半轴为始边,以
所在的射线为终边的角,则
,把
叫做复数
的三角形式,利用复数的三角形式可以进行复数的指数运算,
,例如:
,
,复数
满足:
,则
可能取值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba7cfd25d758444271e0d6466f1810f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8b9ad2fcfff3dd546c5fdbedfe6238.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffea9c467bb7d016c2deda2656d5e84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f54d290009e138d1f0d4cb771cada9f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68164963a78bacd43aebe850e318c81b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd450877ec0f295523ae54c083b74621.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eed3d568acf369a315c7ab41c081049.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9633bd9579b301318eaebe904ded6d62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74d8d2427e2b8ee74f8c4ccbdd54aab7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c210929a917c44bee22f55b1a6b3b599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59c3b8bc6085339a8931950ed206d397.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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3卷引用:福建省龙岩市上杭县第一中学2024届高三下学期5月数学模拟试题
福建省龙岩市上杭县第一中学2024届高三下学期5月数学模拟试题东北三省(哈尔滨师大附中、东北师大附中、辽宁省实验中学)2024届高三第三次联合模拟考试数学试题(已下线)专题07 复数综合题归类(2) -期末考点大串讲(苏教版(2019))
名校
解题方法
4 . 某基层工会拟通过摸球的方式对会员发放节日红包.现在一个不透明的袋子中装有5个都标有红包金额的球,其中有2个球标注的为40元,有2个球标注的为50元,有1个球标注的为60元,除标注金额不同外,其余均相同,每位会员从袋中一次摸出1个球,连续摸2次,摸出的球上所标的红包金额之和为该会员所获得的红包总金额.
(1)若每次摸出的球不放回袋中,求一个会员所获得的红包总金额不低于90元的概率;
(2)若每次摸出的球放回袋中,记
为一个会员所获得的红包总金额,求
的分布列和数学期望.
(1)若每次摸出的球不放回袋中,求一个会员所获得的红包总金额不低于90元的概率;
(2)若每次摸出的球放回袋中,记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
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名校
5 . 如图,
,
是圆锥底面圆
的两条互相垂直的直径,过
的平面与
交于点
,若
为
的中点,
,圆锥的体积为
.
;
(2)若圆
上的点
满足
,求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.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/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9774f83067ed956a551bc41adcce0469.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/813b03f3d13783ee2cb12a81ce6fd07b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b9c25a19759b50db93a7f4c6d750ff4.png)
(2)若圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ceaaa537fddde531dcae13a6ab412f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88ef49a4fcf91b1c60bbd38ac51295fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/134ef0b1a2669a09f05bd4dc2496f706.png)
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名校
解题方法
6 . 设
为函数
在区间
的两个零点,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aca579894dad67bc82cb715fd48e0d70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af3e4a97fb51ed5bc70840e4c46e1e3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/083479b94380e8d659eff92d10a1989d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/928b2ef15bfb97b4a7f998a2bcbe9474.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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7 . 已知正方体
的棱长为3,P在棱
上,
为
的中点,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0424446817f60c18f8e4e3cc202ad99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4818e676741d98793bfd0c496fe7cd39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
A.当![]() ![]() ![]() ![]() | B.当![]() ![]() ![]() |
C.三棱锥![]() | D.![]() ![]() ![]() |
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4卷引用:福建省龙岩市上杭县第一中学2024届高三下学期5月数学模拟试题
福建省龙岩市上杭县第一中学2024届高三下学期5月数学模拟试题黑龙江省齐齐哈尔市2024届高三下学期三模联考数学试卷2024年辽宁省普通高等学校招生全国统一考试(模拟1)数学试题(已下线)专题3 立体几何中的范围、最值问题【练】
名校
8 . 已知函数
,则不等式
的解集为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08bb2ab7f317ad04bedf95fd3933eea1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c90edc2a4e9ffd286afb257225d12ceb.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
9 . 设等差数列
的公差为
,令
,记
分别为数列
的前
项和.
(1)若
,求数列
的通项公式;
(2)若数列
是公比为正数的等比数列,
,
,求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b59214a46d47d4e9d45288588f8f737f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d11aca5961a67d5aee3c03821ffad086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/478421b81927e435cbcf5acafa89efd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62e567d7e9761951a266953c8d5042ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b813b18bbb5bd16c3d6cb6da3790931.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8850b13e872f581e16d8ebba91575b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/847179a6e6e1a1268ab173586e4c8ca6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/749a622e0249b075373103eb31ff50dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
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解题方法
10 . 已知
,则
的值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71dddf05bd9986e353f734f1514b843f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58f04d44d8e08c76a9f5bc24413cf49b.png)
A.![]() | B.![]() | C.![]() | D.2 |
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