19-20高二下·上海浦东新·期末
名校
1 . 已知集合
,其中
,
,
,
表示![](https://staticzujuan.xkw.com/quesimg/Upload/formula/059a6c5a965c335b8da05e697da2c7c2.png)
中所有不同值的个数.
(1)设集合
,
,分别求
,
;
(2)若集合![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce2c8cdc0ae739e1b23ba9a2102dc6fe.png)
,证:
;
(3)
是否存在最小值?若存在,求出这个最小值;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67d35d7c81c3ade827a43c4ab0fac265.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/147a9ae90baacb72de0596be4f69bc2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ef835c9ad2636a9662fb6c99e3abc78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9153fb853cd99beec9e600a4eaf73fe8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f287eeb047884b44460a1c8e73726d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/059a6c5a965c335b8da05e697da2c7c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/349e6582f21958073a3eb0f1fe70eb86.png)
(1)设集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ca112f43de2fa7e39011fe5c90720ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1b831331392b487ce85fa0ac900dba4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c018c9e6ed11bfb122fcf174551b9a97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ead4078398b07739ac40fc10ee8f37eb.png)
(2)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce2c8cdc0ae739e1b23ba9a2102dc6fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9673d71028e49069884d043015d1d87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b0190b02ea4b1ce5dfd703651d23aa3.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f287eeb047884b44460a1c8e73726d5.png)
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2 . 我们称
元有序实数组
为n维向量,
为该向量的范数,已知n维向量
,其中
,
,记范数为奇数的n维向量
的个数为
,这
个向量的范数之和为
.
(1)求
和
的值;
(2)求
的值;
(3)当n为奇数时,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e6bcebb8c5312b69bbac7a3e31e9a88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0df13f8babcb866be14c34b24f38aeac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc452ab5e7b1ba5806bfa8c69cbc490.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14036b9734b313d60766452a29647a73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c7ab835590621ce5227b3bd1fa62b18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ee1569b400d0560d7c42228ad9df6f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a92e6eba8dab638fd66831cd3a0b6d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63f5c583c98a1fd516c6ceaa60b55dec.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a71fc9c0068109dad1382354570665.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13be09bf71dd0a444716121e801cfaed.png)
(3)当n为奇数时,证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2069e78d6c5eee0ec57d089f58f9a1cf.png)
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名校
3 . 设
为给定的大于2的正整数,集合
,已知数列
:
,
,…,
满足条件:
①当
时,
;
②当
时,
.
如果对于
,有
,则称
为数列
的一个逆序对.记数列
的所有逆序对的个数为
.
(1)若
,写出所有可能的数列
;
(2)若
,求数列
的个数;
(3)对于满足条件的一切数列
,求所有
的算术平均值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5de998be2d94d13a52c269c53d2cdfe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3282e5fde4ae53fcb1bb072a685304c9.png)
①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ef835c9ad2636a9662fb6c99e3abc78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d09ca387c74ea67a69c5d757aff4471e.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/937c09d82c480e4d67f8a48d3f66c5f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8ed8bcecf6762164c9f8894942d5083.png)
如果对于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/937c09d82c480e4d67f8a48d3f66c5f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2579fa4a2b6e97fdbe67d24f2f9bc78e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4eeb7fac3defece6a8d27d1b5fe83fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fb1d7f5c0fa9fbdc9be0378ab5e5c45.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fc2b50e81054df70a5f19c266d4f92e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e47cd514b2920609e3781c87df6ab70.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7332e4af9bac83f37bd78351ae70769.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
(3)对于满足条件的一切数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fb1d7f5c0fa9fbdc9be0378ab5e5c45.png)
您最近一年使用:0次
2020-05-01更新
|
970次组卷
|
6卷引用:2020届北京市清华附中高三第二学期第三次统练数学试题
2020届北京市清华附中高三第二学期第三次统练数学试题2020届北京市八一中学高三数学四月份统练试题北京市清华大学附属中学2019~2020学年高二下学期期中考试数学试题(已下线)专题09 计数原理与概率统计-【备战高考】2021年高三数学高考复习刷题宝典(压轴题专练)(已下线)第6章 计数原理(新文化与压轴30题专练)2021-2022学年高二数学下学期考试满分全攻略(人教A版2019选修第二册+第三册)(已下线)高二数学下学期期中精选50题(压轴版)2021-2022学年高二数学下学期考试满分全攻略(人教A版2019选修第二册+第三册)
4 . 我们称n(
)元有序实数组(
,
,…,
)为n维向量,
为该向量的范数.已知n维向量
,其中
,
,2,…,n.记范数为奇数的n维向量
的个数为
,这
个向量的范数之和为
.
(1)求
和
的值;
(2)当n为偶数时,求
,
(用n表示).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e97769855336d73371930df1f187875e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3282e5fde4ae53fcb1bb072a685304c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f8d599542cde6fc27cc4a6f3e7510f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1088503372929503accfe3b02f3365a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38a1efdf5e172ab6f9d63fdef25671ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c45176df950dfe48b8ca7eac08ee349.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb80eb942aafb194fadc473776f35b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63f5c583c98a1fd516c6ceaa60b55dec.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a71fc9c0068109dad1382354570665.png)
(2)当n为偶数时,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63f5c583c98a1fd516c6ceaa60b55dec.png)
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名校
5 . 定义:若数列
满足所有的项均由
构成且其中
有
个,
有
个
,则称
为“
﹣数列”.
(1)
为“
﹣数列”
中的任意三项,则使得
的取法有多少种?
(2)
为“
﹣数列”
中的任意三项,则存在多少正整数
对使得
且
的概率为
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d06f91e41e15def7fb25fc414a61c25c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03f8e95068bff1e6996b11bdb6db4d35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efc4e59d78b78be8c26e2af46867a5f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e267e7a1eb5039bd51c106a7f189a85.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e0842e5153f67ede52f4242b1d7a81c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad42625f296d2a4b65180e2f7b776beb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa8629596367c75b1b35d4f6816b17ca.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e0842e5153f67ede52f4242b1d7a81c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e267e7a1eb5039bd51c106a7f189a85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e267e7a1eb5039bd51c106a7f189a85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ee1b419cf79cf0cf12bdef404238fb4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51ce2b0d668aa3784cf88a0dc398d2b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
您最近一年使用:0次
2020-04-08更新
|
744次组卷
|
2卷引用:2020届江苏省镇江市九校高三下学期3月模拟考试数学试题
6 . 在集合
中,任取
个元素构成集合
.若
的所有元素之和为偶数,则称
为集合
的偶子集,其个数记为
;若
的所有元素之和为奇数,则称
为集合
的奇子集,其个数记为
.
(1)求
,
的值;
(2)求
;(结果用含
的多项式表示)
(3)当
为偶数时,证明:
+
=
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1cc63028c8858be8ec2f4d071c3a019.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b9ad0fa498189f3821045b99f8980b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a0d7559d8dfa8236ca9d4b1853fbdec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a0d7559d8dfa8236ca9d4b1853fbdec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a0d7559d8dfa8236ca9d4b1853fbdec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a33588ff0aa3fcc6efafc5a5a99ba90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a0d7559d8dfa8236ca9d4b1853fbdec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a0d7559d8dfa8236ca9d4b1853fbdec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b78cd844b6fce430ef28c2b5e760e3f7.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc76acb40775f16af461f74d29efdb65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d59b0f0ee3731e6dbb3899e56a6d163.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66afb8918fa1fecdf44f5075ce17e80e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a54b0a5c5422dc0c0ce1eb61de371694.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92b990adae52d73e957230785359538e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3f9ee40504cd3b0a8cf9117d353d101.png)
您最近一年使用:0次
7 . 考查
所有排列,将每种排列视为一个
元有序实数组
,设
且
,设
为
的最大项,其中
.记数组
为
.例如,
时,
;
时,
.若数组
中的不同元素个数为2.
(1)若
,求所有
元有序实数组
的个数;
(2)求所有
元有序实数组
的个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb30e150b60cac09a03dd1fb72eb7941.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b82d71dc477a538b05de6574c91868e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/233427826eb2233641fc3a9805f6d206.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dc54af0d6400579485cbd4e59ac9df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4af42989d172bdc7bfe1cf28822189b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47a84b137ec7bdb19c578ebd079b48c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58fbae1f3d87579b58c64f4768a871eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c7d2e9ce6efea9061ecff3607f10cb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/460410988196e1cdd34c08027766187a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01dbd048c482be3b79e926b66e56062f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fac3649308b528fd56545ba102dc42d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b82d71dc477a538b05de6574c91868e7.png)
(2)求所有
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b82d71dc477a538b05de6574c91868e7.png)
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8 . 设正整数
,集合
,
是集合P的3个非空子集,记
为所有满足:
的有序集合对(A,B,C)的个数.
(1)求
;
(2)求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbf41b2793efa0b332fe039341370ce0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02aac9ee9a68059dd93af7d6e7517561.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://img.xkw.com/dksih/QBM/2019/7/11/2244569768509440/2244614889267200/STEM/76f2937c00b84d4eaaa52d7c80e4996e.png?resizew=213)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
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9 . 平面上有
个点,将每一个点染上红色或蓝色.从这
个点中,任取
个点,记
个点颜色相同的所有不同取法总数为
.
(1)若
,求
的最小值;
(2)若
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb95310306063d4c4df033d37369c219.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2d51f9147b8265c0276c1f2c2659197.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be604061cf1591f7069472269d4c9719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5818ede14d21f6df9ef9c2bfe09286c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5a9aa927638f1b2fc0ea58a533c4f0f.png)
您最近一年使用:0次
10 . 设整数数列{an}共有2n(
)项,满足
,
,且
(
).
(1)当
时,写出满足条件的数列的个数;
(2)当
时,求满足条件的数列的个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/484945dc28f9e331cd12e19e2abf4e8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9cedb02089fef906e1a51376be754fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92fb991597719e079f62b3ab64fcb458.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e76bd4c49bf39a8b627df70e6adf866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/772500049d431f5a20c43e37cf9a518c.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be604061cf1591f7069472269d4c9719.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/561cdfac20ab4159bc7740a680595d15.png)
您最近一年使用:0次
2019-03-22更新
|
1195次组卷
|
3卷引用:【校级联考】江苏省南通市基地学校2019届高三3月联考数学试题