名校
解题方法
1 . 在三维空间中,立方体的坐标可用三维坐标
表示,其中
.而在n维空间中
,以单位长度为边长的“立方体”的顶点坐标可表示为n维坐标
,其中
.现有如下定义:在n维空间中两点间的曼哈顿距离为两点
与
坐标差的绝对值之和,即为
.回答下列问题:
(1)求出n维“立方体”的顶点数;
(2)在n维“立方体”中任取两个不同顶点,记随机变量X为所取两点间的曼哈顿距离
①求出X的分布列与期望;
②证明:在n足够大时,随机变量X的方差小于
.
(已知对于正态分布
,P随X变化关系可表示为
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/121b0b5a52dbbc092104491b0a7a0d1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c332319a3642fd31c04ea47946fde52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e99acf81317c3a6dbca671b1829e21fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4da8c6f3f39586198728a2c2c8cdc69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dca54b04405fb34773eb8fc10328dd38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4da8c6f3f39586198728a2c2c8cdc69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5192fe1adb815a1d043b1c5b15ff64c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/176073f47d770cd7a80d067861b6621d.png)
(1)求出n维“立方体”的顶点数;
(2)在n维“立方体”中任取两个不同顶点,记随机变量X为所取两点间的曼哈顿距离
①求出X的分布列与期望;
②证明:在n足够大时,随机变量X的方差小于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/964e5cf368162d560529c915969d9bc2.png)
(已知对于正态分布
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8471b1bd5c53256f122a0f57d6ecf628.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14356827d3371b5466ba4b9e73dead7a.png)
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2023-08-25更新
|
2008次组卷
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6卷引用:四川省成都市第七中学(高新校区)2024届高三上学期入学考试数学(理科)试题
四川省成都市第七中学(高新校区)2024届高三上学期入学考试数学(理科)试题广东省广州市真光中学2024届高三上学期9月月考数学试题江苏省扬州市扬州中学2024届新高考一卷数学模拟测试一(已下线)专题22 新高考新题型第19题新定义压轴解答题归纳(9大题型)(练习)(已下线)黄金卷08(2024新题型)黑龙江省哈尔滨市双城区兆麟中学2023-2024学年高二下学期第二次月考(6月)数学试题
2 . 在相距2000m的两个观察站A,B先后听到远处传来的爆炸声,已知A站听到的时间比B站早4s,声速是340m/s.建立适当的平面直角坐标系,判断爆炸点可能分布在什么样的轨迹上,并求该轨迹的方程.
您最近一年使用:0次
2023-08-18更新
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218次组卷
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4卷引用:上海市金汇高级中学2022-2023学年高二下学期3月月考数学试题
解题方法
3 . 某农场为了改善水利设施,需要修筑一条横截面为等腰梯形的灌溉水渠,如图所示,已知水渠长400m,深1.5m,渠底宽1m,渠面宽2m.
(1)修筑水渠需要挖出多少立方米的土?
(2)若在水渠的底部和侧面铺设水泥板,则需要的水泥板面积是多少(保留整数,且
)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/4/6683ae97-ac1d-423a-82af-8939dd4248f4.png?resizew=320)
(1)修筑水渠需要挖出多少立方米的土?
(2)若在水渠的底部和侧面铺设水泥板,则需要的水泥板面积是多少(保留整数,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d360e00abad4525101b78f04e1137a8.png)
您最近一年使用:0次
名校
4 . 已知定义域为
的函数
满足:对于任意的
,都有
,则称函数
具有性质
.
(1)判断函数
是否具有性质
;(直接写出结论)
(2)已知函数
,判断是否存在
,使函数
具有性质
?若存在,求出
的值;若不存在,说明理由;
(3)设函数
具有性质
,且在区间
上的值域为
.函数
,满足
,且在区间
上有且只有一个零点.求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a1e1b536866f25b17876d22213c6483.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c04bb391e4e42be0b7cfbcb343b3e86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b90d9223ca11fa78563fdd28d0a2b88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69b5b8c4c24eab782174c5cae1b88a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69b5b8c4c24eab782174c5cae1b88a5.png)
(3)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bccd6a6e85bdf500218a3e75b31f3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56ac39ad998ed60ba3d27d0adab882e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b277ae84cb78ef2d4c345648edbf36d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e140c1c3a640d4f9e0bd5107e9602aae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b8ec0ccdb6db6fbaeb1172e281ec22f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee51768777102389dc962e6fd29e0fce.png)
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2023-07-16更新
|
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12卷引用:北京市昌平区2022-2023学年高一下学期期末质量抽测数学试题
北京市昌平区2022-2023学年高一下学期期末质量抽测数学试题(已下线)专题03 条件存在型【讲】【北京版】1(已下线)专题02 结论探索型【讲】【北京版】1河北省部分学校2024届高三上学期摸底考试数学试题(已下线)新题型01 新高考新结构二十一大考点汇总-3(已下线)黄金卷01(2024新题型)辽宁省沈阳市第一二〇中学2023-2024学年高一下学期第一次月考数学试题(已下线)信息必刷卷02黑龙江省齐齐哈尔市2024届高三下学期联合考试模拟预测数学试题福建省福州第三中学2023-2024学年高三下学期第十六次检测(三模)数学试题【北京专用】专题04三角函数(第四部分)-高一下学期名校期末好题汇编河南省开封市五县六校2023-2024学年高二下学期6月联考数学试题
5 . 定义一种新的运算“
”:
,都有
.
(1)对于任意实数a,b,c,试判断
与
的大小关系;
(2)若关于x的不等式
的解集中的整数恰有3个,求实数a的取值范围;
(3)已知函数
,
,若对任意的
,总存在
,使得
,求实数m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c3c2f679d53b91088ba6eb14c16cbc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2671f593186fa00f17ad26eba7b8f3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a8c23336002eb5d7c478479fcda799f.png)
(1)对于任意实数a,b,c,试判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fda9c56c7993236c0ebdfe08d110ce9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b98e8a20e1e3d328265269df6b2927ad.png)
(2)若关于x的不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b80fef6a2dd7e822d83ae45ea79a5357.png)
(3)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06fc1f7733bebb86885b6e6fd0534e1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d8b60555f0d82c386c5b935c23ff952.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12965bbc260bdbb0df0a110e59fb8d78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93bf66ef253242900ca1702121238b14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52dc0bb1b1d25a0e86babc0edc627e44.png)
您最近一年使用:0次
2023-07-11更新
|
528次组卷
|
3卷引用:山东省青岛市莱西市2022-2023学年高二下学期期末数学试题
名校
解题方法
6 . 函数
的定义域为D,若存在正实数k,对任意的
,总有
,则称函数
具有性质
.
(1)判断下列函数是否具有性质
,并说明理由;
①
;
②
;
(2)已知
为二次函数,若存在正实数k,使得函数
具有性质
.求证:
是偶函数;
(3)已知
,k为给定的正实数,若函数
具有性质
.求a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e02cab1add26335b3cb43d5b54c7c853.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a380348dd1544f954255976659a84a70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daac43c7675fa411b35028e09b0bad90.png)
(1)判断下列函数是否具有性质
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2387880727d458702651d699e76d7d76.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5bc39061e1fb75d8ab1fd5c3765a514.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4306fb6d5419322b4b7b9140e06e43a0.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daac43c7675fa411b35028e09b0bad90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d88a63bbc4eadab1cbce4dbfaf8d411.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daac43c7675fa411b35028e09b0bad90.png)
您最近一年使用:0次
2023-11-24更新
|
237次组卷
|
2卷引用:湖南省长沙市周南中学2022-2023学年高二上学期暑假学习评价检测数学试题
7 . 若数列满足
,则称数列
为“平方递推数列”.已知数列
中,
,点
在函数
的图象上,其中n为正整数,
(1)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e2de706dc5f0439b989273a5367f63a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abdae11d8c18749ce9000613a4afbbb1.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8abdfacf7440d4b455411998085dffe7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bf8e78a4251ded720142a89d83715e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92989b8324c75938a86a26b91a720804.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b783cf91e34e692ce8e171f0965cb53f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
您最近一年使用:0次
2023-05-01更新
|
2253次组卷
|
8卷引用:湖南师范大学附属中学2023届高三二模数学试题
名校
解题方法
8 . 已知椭圆
的方程为
(常数
),点A为椭圆短轴的上顶点,点
是椭圆
上异于点A的一个动点.若动点
到定点A的距离的最大值仅在
点为短轴得另一顶点时取到,则称此椭圆为“圆椭圆”,已知
.
(1)若
,判断椭圆
是否为“圆椭圆”;
(2)若椭圆
是“圆椭圆”,求
的取值范围;
(3)已知椭圆
是“圆椭圆”,且
取最大值,点
关于原点
的对称点为点
(点
也异于点A),且直线
、
分别与
轴交于
、
两点.试问以线段
为直径的圆是否过定点?证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.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/03837b3769eda7f0d3804cc5ad4a6d60.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab839d8569171afab5ed55c22013aa72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
(2)若椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)已知椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.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/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84d454c82d9e52747563d47b68099249.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
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2023-04-13更新
|
288次组卷
|
2卷引用:上海市控江中学2022-2023学年高二下学期3月月考数学试题
9 . 直径为8m的水轮如图所示,水轮圆心
距离水面2m,已知水轮沿逆时针方向匀速旋转,每分钟转动6圈,当水轮上点
从水中浮现时(图中点
)开始计算时间.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/28/997c67ad-168b-4cc8-8a8c-6d199366b9ce.png?resizew=154)
(1)将点
距离水面的高度
表示为时间
的函数;
(2)在水轮转动的一圈内,有多长时间点
在水面下?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf9f50605db5d5f8f3a01ee8e474a112.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/28/997c67ad-168b-4cc8-8a8c-6d199366b9ce.png?resizew=154)
(1)将点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a40420dc952f91a7d333f84771cc7f6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ecd76012d1b9c5e9fec6221e6e489c2.png)
(2)在水轮转动的一圈内,有多长时间点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
您最近一年使用:0次
10 . 若实数
满足
,则称
比
远离
.
(1)若
比
远离1,且
,求实数
的取值范围;
(2)对任意两个不相等的实数
,证明
比
远离
;
(3)若
,试问:
与
哪一个更远离
?并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d32d4403d0e81eacfbe429dc51f07f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b782dd2de9c9caa840838cd63d817de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5558c083d34cbb0a58d3ce1dc6f5778e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)对任意两个不相等的实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17b0bcc077bc78b7aae05b0c9dff42b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb3f034eb004e6db6c58a3bcd7d18cfc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18f0281e6bbdbe08beeccb55adf84536.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45900deae0489e87fe448948e8091c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29ebc856291255f2d4a6c20b982a2442.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
您最近一年使用:0次
2023-08-08更新
|
244次组卷
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2卷引用:江苏省盐城市阜宁县2022-2023学年高一上学期期中数学试题