1 . 由
个数排列成
行
列的数表称为
行
列的矩阵,简称
矩阵,也称为
阶方阵,记作:
其中
表示矩阵
中第
行第
列的数.已知三个
阶方阵分别为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9ff7824ff4c2d54281baa128c63235d.png)
,
,其中
分别表示
中第
行第
列的数.若
,则称
是
生成的线性矩阵.
(1)已知
,若
是
生成的线性矩阵,且
,求
;
(2)已知
,矩阵
,矩阵
是
生成的线性矩阵,且
.
(i)求
;
(ii)已知数列
满足
,数列
满足
,数列
的前
项和记为
,是否存在正整数
,使
成立?若存在,求出所有的正整数对
;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/767f5a4746f04db68386fac3970b1ed1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/767f5a4746f04db68386fac3970b1ed1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3f2dee59acd8ba55c25c9f5316ed3c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04b540e0e8df1cc4f59180460e7d4264.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7600d2cfbdc6146db96cc545706004f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9ff7824ff4c2d54281baa128c63235d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d39d394642b16525e70ecda2fd70cdb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0419a2c0acbb1af2d84373cca6d605a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d37e026f409868f81064617a4120e73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61cbe82b97961a419f24e40bf54a1376.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7600d2cfbdc6146db96cc545706004f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddff15b8d9a8b8f371670b3cba489b4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d03e28332446eea06a9bd61050d38373.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c62349070fb07aaeffbb5d7d91289a9.png)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab241dfd5146035044bc35dcfb3e0994.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/647c97da671781944dcbac93af7cadcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64bb2b9e1f49aee4f4b91f0ba229fd75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28b7d9aa89f698d7ac2772dbf24a5a1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/647c97da671781944dcbac93af7cadcb.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4246c1e8163f564afaf51cec2352362e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18ce6091ca3c6c454219a36f5396ccfa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d03e28332446eea06a9bd61050d38373.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c62349070fb07aaeffbb5d7d91289a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18d7859dc8659a974ea86d14b6ef18e6.png)
(i)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c07cbe067882d2f964195527ad1b33c.png)
(ii)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44a8100f98999e472945ab7050af50d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b783cf91e34e692ce8e171f0965cb53f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa7ffcaea39899aa3e4a17f9a5bc46f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b783cf91e34e692ce8e171f0965cb53f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280860dd039e1305a5ccc455f63e8223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdd0bd4520a95ff89c01f5db5d0a0b0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a64d924836b4292239d9726c6473d7f5.png)
您最近一年使用:0次
名校
解题方法
2 . 如图1,在梯形
中,
,过
分别作梯形的高
,交
于点![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c739074553618fbb8d242ca53976384.png)
,沿
所在直线将梯形折叠,使得点
与点
重合,记为点
,如图2,M是
中点,
是
中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/27/5214425d-ec5b-4e0a-821b-ddf877a78e21.png?resizew=355)
(1)证明:直线![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
平面
;
(2)
是线段
上异于端点的一点,从条件①、条件②、条件③中选择一个作为已知,求平面
与平面
的夹角的余弦值.
条件①:
;
条件②:四棱锥
的体积为
;
条件③:点
到平面
的距离为
;
注:如果选择多个条件分别解答,按第一个解答计分.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34e0a957a55460c72673c0f2ee90dbb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab609a6574633ebabcff3e73fa862081.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/925b8db9b6ed790adf04a5dff4e0e61a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c739074553618fbb8d242ca53976384.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40be06d1ee73fd02f0a6039081dc4c5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/925b8db9b6ed790adf04a5dff4e0e61a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fb26d84907c923278ac4626a9d58947.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/27/5214425d-ec5b-4e0a-821b-ddf877a78e21.png?resizew=355)
(1)证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4739ad948445af72d585fe29c745929b.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/149596fee6ed1e2d19fd8dadc14a8baf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c5a4dfcf4c24a8ecb210cc4c53db221.png)
条件①:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74d761129d39626d79053680475caba8.png)
条件②:四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/504c7cd04dc84c872e5539d9906bd36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf31876698721a199c7c53c6b320aa86.png)
条件③:点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d246f9eceab371ebf47a47c2f11a4ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4b8503f4706b8321e4e79a87eadea84.png)
注:如果选择多个条件分别解答,按第一个解答计分.
您最近一年使用:0次
名校
3 . 某中学有高一年级学生600人,高二年级学生400人参加知识竞赛,现用分层抽样的方法从中抽取100名学生,对其成绩进行统计分析.得到如下图所示的频率分布直方图.
(1)求从该校高一年级、高二年级学生中各抽取的人数;
(2)根据频率分布直方图,估计该校这1000名学生中竞赛成绩在60分(含60分)以上的人数.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/26/c6badc6c-da5b-450c-9feb-0b4de993a39d.png?resizew=225)
(1)求从该校高一年级、高二年级学生中各抽取的人数;
(2)根据频率分布直方图,估计该校这1000名学生中竞赛成绩在60分(含60分)以上的人数.
您最近一年使用:0次
2023-07-22更新
|
764次组卷
|
5卷引用:海南省定安县定安中学2024届高三上学期开学考试数学试题
海南省定安县定安中学2024届高三上学期开学考试数学试题(已下线)高一数学开学摸底考 01-北师大版2019必修第一册全册开学摸底考试卷新疆维吾尔自治区塔城市第三中学2022-2023学年高二下学期7月期末数学试题9.2.1总体取值规律的估计练习上海市徐汇区2023-2024学年高二上学期期末统考数学试卷
4 . 如图,在平面直角坐标系中,抛物线y=ax2+bx-3经过点
和点
,与x轴的另一个交点为A,与y轴交于点C,作直线AD.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/27/2b0b334c-7e94-4d9e-8945-321e7da72d88.png?resizew=213)
(1)①求抛物线的函数表达式;②写出直线AD的函数表达式;
(2)点E是直线AD下方的抛物线上一点,连接BE交AD于点F,连接BD,DE,△BDF的面积记为S1,△DEF的面积记为S2,当S1=2S2时,求点E的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8df87c934ddd8db630f49c3bd161c0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58a6f455f82c7744ee80c5d6ff3e8ffd.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/27/2b0b334c-7e94-4d9e-8945-321e7da72d88.png?resizew=213)
(1)①求抛物线的函数表达式;②写出直线AD的函数表达式;
(2)点E是直线AD下方的抛物线上一点,连接BE交AD于点F,连接BD,DE,△BDF的面积记为S1,△DEF的面积记为S2,当S1=2S2时,求点E的坐标.
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5 . 某公司要在甲、乙两人中招聘一名职员,对两人的学历,能力、经验这三项进行了测试.各项满分均为10分,成绩高者被录用.图1是甲、乙测试成绩的条形统计图,
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/28/cb2ed1ec-5b9f-4321-be6b-377a5b5b410a.png?resizew=414)
(1)分别求出甲、乙三项成绩之和,并指出会录用谁;
(2)若将甲、乙的三项测试成绩,按照扇形统计图(图
各项所占之比,分别计算两人各自的综合成绩,并判断是否会改变(1)的录用结果.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/28/cb2ed1ec-5b9f-4321-be6b-377a5b5b410a.png?resizew=414)
(1)分别求出甲、乙三项成绩之和,并指出会录用谁;
(2)若将甲、乙的三项测试成绩,按照扇形统计图(图
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca778d559493146e7a57af60ae937825.png)
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6 . 2022年北京冬奥会吉祥物冰墩墩和冬残奥会吉祥物雪容融深受大家喜爱.已知购买1个冰墩墩毛绒玩具和2个雪容融毛绒玩具用了400元,购买3个冰墩墩毛绒玩具和4个雪容融毛绒玩具用了1000元.这两种毛绒玩具的单价各是多少元?
您最近一年使用:0次
7 . 已知
.
(1)化简
;
(2)若正方形
的边长为
,且它的面积为9,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dddb8a8369f1f347c5d0efc3cc2251b.png)
(1)化简
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67300207553ae70b997bde84ca730cf8.png)
(2)若正方形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4887473a8091e1ef53a169cc9f211e3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67300207553ae70b997bde84ca730cf8.png)
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8 . 某市为鼓励居民节约用电,采用阶梯电价的收费方式,当月用电量不超过100度的部分,按0.4元/度收费;超过100度的部分,按0.8元/度收费.
(1)若某户居民用电量为120度,则该月电费为多少元?
(2)若某户居民某月电费为60元,则其用电量为多少度?
(1)若某户居民用电量为120度,则该月电费为多少元?
(2)若某户居民某月电费为60元,则其用电量为多少度?
您最近一年使用:0次
2022-10-23更新
|
781次组卷
|
4卷引用:海南省乐东黎族自治县华东师范大学第二附属中学乐东黄流中学2023-2024学年高一下学期开学摸底考试数学试题
解题方法
9 . 甲、乙、丙三人进行围棋比赛,规则如下:甲、乙进行第一局比赛,丙旁观;每局比赛的胜者与旁观者进行下一局比赛,负者下一局旁观;直至有人累计胜两局,则比赛结束,且先累计胜两局者为本次比赛获胜者.已知甲乙对弈,每局双方获胜的概率均为0.5,甲丙对弈、乙丙对弈,每局丙获胜的概率均为0.4、对方获胜的概率均为0.6,各局比赛结果相互独立.
(1)设本次比赛共进行了X局,求X的分布列与数学期望;
(2)若比赛结束时共进行了4局对弈,求丙是本次比赛获胜者的概率.
(1)设本次比赛共进行了X局,求X的分布列与数学期望;
(2)若比赛结束时共进行了4局对弈,求丙是本次比赛获胜者的概率.
您最近一年使用:0次
2022-09-07更新
|
408次组卷
|
3卷引用:海南省海口中学2023届高三上学期9月摸底考试数学试题