1 . 设数列
:
,
,
,…,
(
,
),如果
中各项按一定顺序进行一个排列,就得到一个有序数组
:(
,
,
,…,
).若有序数组
:(
,
,
,…,
)满足
恒成立,则称
:(
,
,
,…,
)为
阶减距数组;若有序数组
:(
,
,
,…,
)满足
恒成立,则称
:(
,
,
,…,
)为
阶非减距数组.
(1)已知数列
:
,3,2,
,请直接写出该数列中的数组成的所有4阶减距数组;
(2)设
:(
,
,
,…,
)是数列
:1,3,5,…,
(
,
)的一个有序数组,若
:(
,
,
,…,
)为
阶非减距数组,且
:(
,
,…,
)为
阶非减距数组,请直接写出4个满足上述条件的有序数组
;
(3)已知等比数列
:
,
,
,…,
(
)的公比为
,证明:当
时,
:(
,
,
,…,
)为
阶非减距数组.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.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/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cca1d86c9f078347773f700fee49d1d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b715e7842b95f654f16056a7c7f2abe9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13423c094861baf4b759b7f3d8c3c226.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57483e04fd1840c87ac5325157149877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b715e7842b95f654f16056a7c7f2abe9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13423c094861baf4b759b7f3d8c3c226.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57483e04fd1840c87ac5325157149877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/103b260482483a50c92a898a4f8d0d69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b715e7842b95f654f16056a7c7f2abe9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13423c094861baf4b759b7f3d8c3c226.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57483e04fd1840c87ac5325157149877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b715e7842b95f654f16056a7c7f2abe9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13423c094861baf4b759b7f3d8c3c226.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57483e04fd1840c87ac5325157149877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11851a3bcf106a6c6a47c77bf6346f06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b715e7842b95f654f16056a7c7f2abe9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13423c094861baf4b759b7f3d8c3c226.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57483e04fd1840c87ac5325157149877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(1)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81fb134b2b48acc99213fff6ccfee65f.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b715e7842b95f654f16056a7c7f2abe9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13423c094861baf4b759b7f3d8c3c226.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57483e04fd1840c87ac5325157149877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/627a57cd9fdb1f586f35d9825b6bcc0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5818ede14d21f6df9ef9c2bfe09286c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cca1d86c9f078347773f700fee49d1d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b715e7842b95f654f16056a7c7f2abe9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13423c094861baf4b759b7f3d8c3c226.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57483e04fd1840c87ac5325157149877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5105d6cd72f7b03ffb9d623d348b5b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b715e7842b95f654f16056a7c7f2abe9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13423c094861baf4b759b7f3d8c3c226.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e9d41db805f5235ec4b69e436690222.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96e66fef6fd59fd11929c390d5b12dcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
(3)已知等比数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.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/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f71acdb04454c77e1e25ad4f336cccfe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.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/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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2 . 设函数
为定义在区间
上的可导函数,记
的导函数为
,若对
,都有
或
恒成立,则称
为区间
上的“原导同号函数”.
(1)证明:
为
上的“原导同号函数”;
(2)是否存在实数
,使
为
上的“原导同号函数”,若存在,求出
的取值范围;若不存在,请说明理由;
(3)若
为
上的“原导同号函数”,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc1da2db85b44ae9ced8c09cd19593e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/126f7f1e8cdd38225803c6ec59968660.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22a935456da83aed9c3f485152e541f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36489856ced75bf35dea7b12c2b6bcd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5d6243e93c41978871cb23d8e66148d.png)
(2)是否存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b14ce24da9de20311832866834d78a05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5d6243e93c41978871cb23d8e66148d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6146c34c9aad4d49938e086d3b18c774.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8845c0d06613fabb0358d5392cca38b3.png)
您最近一年使用:0次
名校
3 . 孟德尔在观察豌豆杂交时发现了以下规律:豌豆的各种性状是由其遗传因子决定的. 以子叶颜色为例,豌豆的子叶分黄、绿两种颜色,其中黄色为显性性状,绿色为隐性性状. 我们用
表示子叶为黄色的豌豆的遗传因子对,用
表示子叶为绿色的豌豆的遗传因子对. 当这两种豌豆杂交时,父本的其中一个遗传因子与母本的其中一个遗传因子等概率随机组合,子一代的遗传因子对全部为
,如图所示,其中
为显性遗传因子,
为隐性遗传因子. 当生物的遗传因子对中含有显性遗传因子时呈现显性性状,否则呈现隐性性状. 例如:
均指示黄色子叶,
指示绿色子叶. 我们称以上定律为孟德尔定律.
与
)进行交配得到子三代豌豆,求子三代豌豆中子叶颜色为绿色的概率.
(2)已知人的单、双眼皮性状服从孟德尔定律,其中双眼皮是显性性状,记其遗传因子对为
或
;单眼皮是隐性性状,记其遗传因子对为
. 若仅考虑眼皮性状,已知你的祖父、祖母和母亲的遗传因子对均为
:
(ⅰ)在你是双眼皮的条件下,求父亲是单眼皮的概率;
(ⅱ)祖父和祖母育有伯父、父亲、叔父和姑母三子一女,除父亲外,其余三人均与单眼皮配偶婚配并各育有一子,求你及你的三代以内父系亲属(如图)中双眼皮人数的数学期望.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b95a9bdde17eba7e522d1e3850171a85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09b012d39bca448ca6d2f2563095af11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e122c4ec85171d39684543de1484b74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b51c2660cbc2a1d78e3f00dd91d9a51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09b012d39bca448ca6d2f2563095af11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b95a9bdde17eba7e522d1e3850171a85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b95a9bdde17eba7e522d1e3850171a85.png)
(2)已知人的单、双眼皮性状服从孟德尔定律,其中双眼皮是显性性状,记其遗传因子对为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94c56378a35ea2dc824e60450356eba4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdacfce5b9dc683d4f742b3aad24c22b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2441066b8a4db9e679e4ef61ecf1da4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdacfce5b9dc683d4f742b3aad24c22b.png)
(ⅰ)在你是双眼皮的条件下,求父亲是单眼皮的概率;
(ⅱ)祖父和祖母育有伯父、父亲、叔父和姑母三子一女,除父亲外,其余三人均与单眼皮配偶婚配并各育有一子,求你及你的三代以内父系亲属(如图)中双眼皮人数的数学期望.
您最近一年使用:0次
解题方法
4 . 若一个两位正整数
的个位数为6,则称
为“幸运数”.
(1)对任意“幸运数”
,证明:
能被6整除;
(2)已知集合
.
①若
,证明:
;
②若“幸运数”
,则称数对
为“亲密数对”,规定:
,求小于50的“幸运数”中,所有“亲密数对”的
的所有值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(1)对任意“幸运数”
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6b044c1df8d6021eccebd4e9120f232.png)
(2)已知集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45e5dc7f66a23728165409821aaca1b3.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcf58d3883bcd6273dc624a0abef69f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d783f369011a6d18f3b14c8d8ed171fb.png)
②若“幸运数”
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a0ac8b620b5eca9daa7276712935ef6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/698c4d4e50062b4a7dd70fe1b4ab4fd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04e0d26b41dcdbe19680eade8702c0a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8f884759486947e0215402e45ed0a2e.png)
您最近一年使用:0次
解题方法
5 . 球面几何在研究球体定位等问题有重要的基础作用.球面上的线是弯曲的,不存在直线,连接球面上任意两点有无数条曲线,它们长短不一,其中这两点在球面上的最短路径的长度称为两点间的球面距离.
纬线,赤道以北叫做北纬.如图1,将地球看作球体,假设地球半径为
,球心为
,北纬
的纬线所形成的圆设为圆
,且
是圆
的直径,球面被经过球心
和点
,
的平面截得的圆设为圆
,求圆
中劣弧
的长度,并判断其是否是
,
两点间的球面距离(只需判断、无需证明).
(2)如图2,点
,
在球心为
的球面上,且
不是球的直径,试问
,
两点间的球面距离所在的圆弧
是否与球心
共面?若是,写出证明过程,并求出当
,
时,
,
两点间球面距离所在的圆弧
与球心
所形成的扇形
的面积;若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/235d495d88b8e51f89e2e4da27328025.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6b86c22b670a8e9f3896f9e8883fbbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12fe32dfbd66709875c5b9f79c9496da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bb0628cecbfc98d390e5447d52414e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12fe32dfbd66709875c5b9f79c9496da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c314398e26ffc7164b82946eeb4273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3953cec61ac602ce5eb59b7912352179.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/240d929040e21e7991481149b73a79a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c314398e26ffc7164b82946eeb4273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3953cec61ac602ce5eb59b7912352179.png)
(2)如图2,点
![](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/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.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/16d65cecaf8a3dc2953f4109c75a981e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c93ef48e154646ef0564de14a990c2e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c467c10aa2eabce3af68c1213d88043b.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/16d65cecaf8a3dc2953f4109c75a981e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c880639a6164aa127cf38b63aebde50.png)
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名校
解题方法
6 . 如图,圆柱
的底面半径为1,侧面积为
,
,
分别是圆柱上、下底面圆的一条直径,且点
在下底面的投影点
平分圆弧
.
的表面上,求球
的表面积;
(2)求四面体
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e65ac334119ccd6204402a7aba29a55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35e2d7c958e99bcd9d7f251c19ee3544.png)
![](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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c314398e26ffc7164b82946eeb4273.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/1dde8112e8eb968fd042418dd632759e.png)
(2)求四面体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
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2024-05-23更新
|
553次组卷
|
3卷引用:河南省信阳高级中学2023-2024学年高一下学期5月期中考试数学试题
7 . 2024年7月26日至8月11日将在法国巴黎举行夏季奥运会.为了普及奥运知识,M大学举办了一次奥运知识竞赛,竞赛分为初赛与决赛,初赛通过后才能参加决赛
(1)初赛从6道题中任选2题作答,2题均答对则进入决赛.已知这6道题中小王能答对其中4道题,记小王在初赛中答对的题目个数为
,求
的数学期望以及小王在已经答对一题的前提下,仍未进入决赛的概率;
(2)
大学为鼓励大学生踊跃参赛并取得佳绩,对进入决赛的参赛大学生给予一定的奖励.奖励规则如下:已进入决赛的参赛大学生允许连续抽奖3次,中奖1次奖励120元,中奖2次奖励180元,中奖3次奖励360元,若3次均未中奖,则只奖励60元.假定每次抽奖中奖的概率均为
,且每次是否中奖相互独立.
(i)记一名进入决赛的大学生恰好中奖1次的概率为
,求
的极大值;
(ii)
大学数学系共有9名大学生进入了决赛,若这9名大学生获得的总奖金的期望值不小于1120元,试求此时
的取值范围.
(1)初赛从6道题中任选2题作答,2题均答对则进入决赛.已知这6道题中小王能答对其中4道题,记小王在初赛中答对的题目个数为
![](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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/161cafe3ab0c7b57ed23212f75c407e9.png)
(i)记一名进入决赛的大学生恰好中奖1次的概率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed1f109f79547d6ae0d94339e689e8f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed1f109f79547d6ae0d94339e689e8f7.png)
(ii)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
您最近一年使用:0次
2024-05-20更新
|
2483次组卷
|
3卷引用:河南省三门峡部分名校2024届高三下学期高考模拟考试(一)数学试题
8 . 在直角坐标系
中,已知
,且
.
(1)求点
的轨迹
的方程;
(2)由圆
上任一点
处的切线方程为
,类比其推导思想可得抛物线
上任一点
处的切线方程为
.现过直线
上一点
(不在
轴上)作
的两条切线,切点分别为
,若
分别与
轴交于
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86e3ce51a1e6974dd295f57ebab7532c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2cc1f1ef9ad32eef62aefa4c3fc3d6b.png)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d259822ab64b8626f3893b8432673358.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
(2)由圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d443779a9f5889e921a60e5b452a926f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/128aa322f3e76e8f03a7402bb2b2ae25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2964452515a439993a169480d057c00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e6c830bfa9a1b979a1a9665166424bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/128aa322f3e76e8f03a7402bb2b2ae25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ba380c2fbc3e6c45bb1dc28a15e219a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba53065eb180a682305fddb95d14b62f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8ca00309261a540934d9b3ed9ba05b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a1c951a9d542338bbf10340b889c828.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b1aa30ddc123130f99fd875635022d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f12a06dd374a246257f84b074a84ed2f.png)
您最近一年使用:0次
9 . 函数
称为取整函数,也称为高斯函数,其中
表示不超过实数
的最大整数,例如:
.对于任意的实数
,定义
数列
满足
.
(1)求
的值;
(2)设
,从全体正整数中除去所有
,剩下的正整数按从小到大的顺序排列得到数列
.
①求
的通项公式;
②证明:对任意的
,都有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8aacac2cf1dd70cc65b1ca535a32c316.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2ab85825d4a002600ca41bd3cd2ee7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/622fceaaac153f8160d2f5713a72cd80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e2ab76a638c611caab9d45f581a2103.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee5c947a5d53575afbe7b3b7a5b768fb.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b96734e9f87adadcc936cc88ee51d6a.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c46752bd68b97f8cb69b26e14acdc468.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
②证明:对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/209559aca6bf32705588b6a40e0b7320.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/842662746027171c32a2eda22210ae1d.png)
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10 . 复数除了代数形式
之外,还有两种形式,分别是三角形式和指数形式,著名的欧拉公式
体现了两种形式之间的联系.利用复数的三角形式进行乘法运算,我们可以定义旋转变换.根据
,我们定义:在直角坐标系内,将任一点绕原点逆时针方向旋转
的变换称为旋转角是
的旋转变换.设点
经过旋转角是
的旋转变换下得到的点为
,且旋转变换的表达式为
曲线的旋转变换也如此,比如将“对勾”函数
图象上每一点绕原点逆时针旋转
后就得到双曲线:
.
(1)求点
在旋转角是
的旋转变化下得到的点的坐标;
(2)求曲线
在旋转角是
的旋转变化下所得到的曲线方程;
(3)等边
中,
在曲线
上,求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eed3d568acf369a315c7ab41c081049.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26032c72018539ca7aa3ca66ac845260.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/224921c5f4e35b546b1fa8b65323086b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c65d3d6119b18fd2427497cbd413c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e92cb090fd6e4ce2779ddb11ec365c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98d06619274d7c0e540c0e7dbbdbbfbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1305b9abebd7bef3171486df157286b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5e24f048f9a87274863ba2c037d7a5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55a93855bd1b93f92a6b41da629d6f9d.png)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58f6fb134624fa01a9b3eb651434944d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15615de1a6df206dbd081251f676578e.png)
(2)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/377a2333ff8c63cbdb20b882d6d5a7ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15615de1a6df206dbd081251f676578e.png)
(3)等边
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/894eb4285cb70b66fe2b60a36d07f3ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/377a2333ff8c63cbdb20b882d6d5a7ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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