1 . 已知数列
,记集合
.
(1)对于数列
:1,2,3,4,写出集合T;
(2)若
,是否存在
,使得
?若存在,求出一组符合条件的i,j;若不存在,说明理由;
(3)若
,把集合T中的元素从小到大排列,得到的新数列为B:
,
,…,
,….若
,求m的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46d0184b17069e7bf858caea5e394f90.png)
(1)对于数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9260f8989cfd0ffca5a49ffbc0668f14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e00afc6f1416bbbd6f2b6d19b1f3e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8171c326a953584f90d3a210e7d1c0e0.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a694ee63925fe653457f577063d6d7c.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/0f64696f60c533ad95dc7890eb902741.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25efaf1a568553b27434c71ddb447c9b.png)
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2 . 已知数列
满足
,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
(1)求数列
的通项公式;
(2)记数列
的前
项和为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
①若
,
,
成等比数列,求正整数
的值;
②数列
的前
项和为
,证明
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e579ffa9fe79fcc794606d5b2bb26fc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)记数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f255d0395fba51ca2d44293cca42e0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0620331265c321c19bc86f418a3e014d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
②数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8050391385b496e9c059201e4f12600a.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/9c3fec47d2dd2b8099d86c87b6e57de8.png)
您最近一年使用:0次
名校
解题方法
3 . 已知公差为正数的等差数列满足
成等比数列.
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbd8e16b5cce392a12326fa2f3ee9acd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e554e17bb75fb6ca18e00995a0e9330b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be87365151702d8b0a4f31450637ed15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次
2023-10-17更新
|
577次组卷
|
3卷引用:北京市广渠门中学2024届高三上学期10月考数学试题
北京市广渠门中学2024届高三上学期10月考数学试题(已下线)第05讲 4.3.2等比数列的前n项和公式(7类热点题型讲练)-【帮课堂】2023-2024学年高二数学同步学与练(人教A版2019选择性必修第二册)上海市金山中学2023-2024学年高二下学期3月月考数学试卷
解题方法
4 . 给定数列
,若满足
(
且
),对于任意的
,都有
,则称数列
为“指数型数列”.
(1)已知数列
的通项公式分别为
,试判断数列
是不是“指数型数列”;
(2)已知数列
满足
,判断数列
是不是“指数型数列”.若是,请给出证明,若不是,请说明理由;
(3)若数列
是“指数型数列”,且
,证明数列
中任意三项都不能构成等差数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7fab51121848ce166035ceab6f4e00b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48de37a91f83fbccb2b38982a7a1206b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6659dea324adeae6acec784d60f4882.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62e567d7e9761951a266953c8d5042ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbaa8611a9afffb8fc7f5778c745186f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62e567d7e9761951a266953c8d5042ac.png)
(2)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7aa6ea31495451da2f12c414efe0807d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0143b0d34aed876ff4cad5f92fb861e0.png)
(3)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b6a88cddb19ab2d45a7713829c65ebd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
您最近一年使用:0次
5 . 已知数列
的项数均为m
,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34919e3b413417f8fcc06fbfbca9bfe0.png)
的前n项和分别为
,并规定
.对于
,定义
,其中,
表示数集M中最大的数.
(1)若
,求
的值;
(2)若
,且
,求
;
(3)证明:存在
,满足
使得
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62e567d7e9761951a266953c8d5042ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c53fc8ddaa412b237ecb095cf1c65335.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34919e3b413417f8fcc06fbfbca9bfe0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62e567d7e9761951a266953c8d5042ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b64f109cde567dc5750276a16a6b774.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7d230d1915653fb876373f882ca81b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cd13665a47f5548727c599936b32dc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e2d6df455d7702a81bdbc86f17e8c81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/698f45c9ed5bb04924f1037107e76988.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15dc21f6a796961cc506633a4fe32563.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd374d21bbdff3c6f8e69b557a86e2ce.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/295f2712a68800672db5c617713eedf7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9de2f1a28584f093949cc0b854dfb3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a135cb036833400f3fa1edc92d5ce410.png)
(3)证明:存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a23a3f55b2eb456a65b9788574437678.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/363d7ed2c067c37fb1dfc5e2a50ba573.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1eedada19441233cfac2f4e4322cf85.png)
您最近一年使用:0次
2023-06-19更新
|
10452次组卷
|
19卷引用:2023年北京高考数学真题
2023年北京高考数学真题北京十年真题专题06数列北京市丰台区第二中学2024届高三上学期开学考数学试题北京市第八十中学2023-2024学年高三上学期10月月考数学试卷专题14数列(已下线)五年北京专题10数列(已下线)三年北京专题10数列专题05数列(成品)(已下线)2023年北京高考数学真题变式题16-21(已下线)数列新定义(已下线)专题6.1 等差数列及其前n项和【九大题型】(已下线)重难点10 数列的通项、求和及综合应用【九大题型】(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大核心考点)(讲义)(已下线)专题30 等比数列通项与前n项和(已下线)专题21 数列解答题(理科)-2(已下线)专题21 数列解答题(文科)-3(已下线)专题2 考前押题大猜想6-10专题06数列(已下线)专题05 等比数列与数列综合求和-2023-2024学年高二数学期末复习重难培优与单元检测(人教A版2019)
6 . 已知
为等差数列,
,记
,
分别为数列
,
的前n项和,
,
.
(1)求
的通项公式;
(2)证明:当
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e9840fce9bc9f6bfd4ca69295c133d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19181548bcfbfe7a38a2c84096199563.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf068678969571e78425d6f279cd1995.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45deada38f235bf0efb327bc4477034a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90718ef497edb369828f4b8e323b10d7.png)
您最近一年使用:0次
2023-06-07更新
|
44176次组卷
|
44卷引用:北京市景山学校2024届高三上学期10月月考数学试题
北京市景山学校2024届高三上学期10月月考数学试题2023年新课标全国Ⅱ卷数学真题(已下线)2023年高考数学真题完全解读(新高考Ⅱ卷)专题05数列(成品)专题05数列(添加试题分类成品)专题05数列(成品)(已下线)专题11 数列前n项和的求法 微点8 分组法求和(已下线)2023年新课标全国Ⅱ卷数学真题变式题15-18(已下线)专题07 数列-1(已下线)模块一 情境3 以数列为背景(已下线)重难专攻(五) 数列中的综合问题(讲)山西省晋城市第一中学校2024届高三上学期8月月考数学试题江西省宜春市宜丰县宜丰中学2023-2024学年高三上学期9月月考数学试题天津市耀华中学2024届高三上学期第一次月考数学试题福建省厦门第二中学2024届高三上学期第二次阶段性考试(10月)数学试题(已下线)第05讲 数列求和(练习)(已下线)第02讲 等差数列及其前n项和(十大题型)(讲义)-2(已下线)第04讲 数列的通项公式(练习)-2(已下线)天津市耀华中学2024届高三上学期第一次月考数学试题变式题16-20(已下线)考点3 等差列的前n项和及其性质 2024届高考数学考点总动员(已下线)考点12 数列中的不等关系 2024届高考数学考点总动员(已下线)第2讲:复杂数列通项和求和【练】(已下线)第3讲:数列中的不等问题【练】(已下线)专题04 数列及求和(讲义)(已下线)专题10 数列不等式的放缩问题 (7大核心考点)(讲义)(已下线)专题05 数列 第三讲 数列与不等关系(解密讲义)(已下线)专题05 数列 第二讲 数列的求和(解密讲义)(已下线)专题05 数列 第二讲 数列的求和(分层练)(已下线)专题29 等差数列通项与前n项和(已下线)专题6.1 等差数列及其前n项和【九大题型】(已下线)重难点10 数列的通项、求和及综合应用【九大题型】(已下线)专题06:数列大题真题精练(已下线)专题09 数列的通项公式、数列求和及综合应用(练习)-2天津市九校2024届高三下学期联合模拟考试(一)数学试卷(已下线)FHgkyldyjsx15(已下线)专题21 数列解答题(理科)-3(已下线)专题21 数列解答题(文科)-2(已下线)专题2 考前押题大猜想6-10江苏省无锡市锡东高级中学2024届高三下学期5月月考数学试题专题06数列(已下线)专题05 等比数列与数列综合求和-2023-2024学年高二数学期末复习重难培优与单元检测(人教A版2019)湖南省衡阳市第八中学2023-2024学年高二创新班上学期第一阶段测试数学试题(已下线)重难点03:数列近3年高考真题赏析-2023-2024学年高二数学同步精品课堂(北师大版2019选择性必修第二册)(已下线)重难点02:求数列前n项和常用10种解题策略-2023-2024学年高二数学同步精品课堂(北师大版2019选择性必修第二册)
解题方法
7 . 已知:正整数列
各项均不相同,
,数列
的通项公式![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f44d3c3cbd26b797a70e5fd060f3106.png)
(1)若
,写出一个满足题意的正整数列
的前5项:
(2)若
,求数列
的通项公式;
(3)证明若
,都有
,是否存在不同的正整数
,j,使得
,
为大于1的整数,其中
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de777c4e44546bcfe26ad5b6bb418052.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f44d3c3cbd26b797a70e5fd060f3106.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9a7269903c6005c0645a6033c8c1dd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d11adcab5f73046ada2b4dd21ba74614.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(3)证明若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21d2e7f3d5771184a5a93749368dc2a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f33e3c5a9ab39e55e78d6aef60e5e3d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b97c28585cf80e2b403c8e23ac391573.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2690c409f513b571c3c2548228536d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b204cd055cc01b4fc9dd888b8348d12.png)
您最近一年使用:0次
8 . 正整数集合
,且
,
,
中所有元素和为
,集合
.
(1)若
,请直接写出集合
;
(2)若集合
中有且只有两个元素,求证“
为等差数列”的充分必要条件是“集合
中有
个元素”;
(3)若
,求
的最小值,以及当
取最小值时,
最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59003c6febf1a45fc85bc475a3a17b8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c002c44d45907aad22da19859193270b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75fd9ec9c065d4337a8b1ebf2abc6a1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dd8ff87ff3fef45414f594ae017351e.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98bef20fc87980ef78c7f8eebd15f308.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d02a8555da4dbbc7820a50a95b071ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/629455b181f187fe9b0edd9d66431ef0.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/143d9d0954abea7adb3412216fe8daf7.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/96abfe2da27a63e6affb19a0c80236d9.png)
您最近一年使用:0次
9 . 在公差不为0的等差数列
中,
,且
,
,
成等比数列.
(1)求
的通项公式和前n项和
;
(2)设
,求数列
的前n项和公式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7da6e97248df8f138ebe684c40c950c7.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/5da4cd81500bdb43118150dbdb1541e6.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/216876de04325fd250c38c485cbc34b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
您最近一年使用:0次
2023-05-11更新
|
1635次组卷
|
7卷引用:北京市第八十中学2023-2024学年高三上学期10月月考数学试卷
名校
10 . 若项数为的有穷数列
满足:
,且对任意的
,
或
是数列
中的项,则称数列
具有性质
.
(1)判断数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/612901cfa20b91933cd04ec66178d034.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01a2e57debe5d5a7f31b401597a214b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b88864e70eca93cb07c3912ec6ed926.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
(3)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69fb89a461f270529af6b6675d0287ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
您最近一年使用:0次
2023-05-10更新
|
1219次组卷
|
5卷引用:北京市房山区2023届高三二模数学试题