1 . 如图,在四棱台
中,
平面
,底面
为平行四边形,
,且
分别为线段
的中点.
.
(2)证明:平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fd66687a8c0d2d00ba430b040e9f647.png)
平面
.
(3)若
,当
与平面
所成的角最大时,求四棱台
的体积
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ccc0d735dc14c92a8926d9b1def6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/417104247ce266ae42c3a9860f387272.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8e658d7985a600629fdf01517fc55c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cac18faf9da6221b788020ac0ddf709b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fab0d028634166a93c5d80add98dc27.png)
(2)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fd66687a8c0d2d00ba430b040e9f647.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74bca84ad86c648d3bb20c8909c8da3f.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faec6f7381dbe8daf15b2969f379e3d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74bca84ad86c648d3bb20c8909c8da3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be54e84508decfcce6d2fcbe6c8c1a92.png)
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5卷引用:河南省创新发展联盟2023-2024学年高一下学期第三次月考(5月)数学试题
2 . 已知函数
.
(1)若函数
在其定义域内有两个不同的零点,求实数
的取值范围;
(2)若
,且
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7fd03e2a84a26f821d7c019945fefc5.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d41acc47493556617fe7b9e55093d10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbe4e306e70a98dc5ec24e6e1dfcb392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edd1204aa622a896c55d812d5d1a728d.png)
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名校
3 . 用数学的眼光看世界就能发现很多数学之“美”.现代建筑讲究线条感,曲线之美让人称奇,衡量曲线弯曲程度的重要指标是曲率,曲线的曲率定义如下:若
是
的导函数,
是
的导函数,则曲线
在点
处的曲率
.
在
处的曲率
的平方;
(2)求余弦曲线
曲率
的最大值;
(3)余弦曲线
,若
,判断
在区间
上零点的个数,并写出证明过程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/090a91e4f3c8930674f98a9fa527709b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bac50c92211d6348b056335f6c83ea1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/090a91e4f3c8930674f98a9fa527709b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e669b77945df783df093b549ac2a67d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bdb811e83e6f94b20dfa3ab68b1096.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/391039b1ebf01aa7def8a44c97ea05b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9311b13eb2baab6641da9e7b48e13e24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e029cc1f7d07eeb136bd3946a7eb23e3.png)
(2)求余弦曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/832d87f3c6bd439ef3d84a6c6da3642e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32410867843f1a7ef11410da8f3f8dab.png)
(3)余弦曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/832d87f3c6bd439ef3d84a6c6da3642e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cbffb683ddd3767c5ebd35ac9212f6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/877e6c30566e9d9b11ecf5b78f4c5e73.png)
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解题方法
4 . 已知双曲线
的离心率为
,半焦距为
,
为
的左顶点,直线
.
(1)求
的方程.
(2)若l过定点
,且交
于
,
两点(异于点
),证明:直线
与
的斜率之积为定值.
(3)若
与
有唯一的公共点
,过点
且与
垂直的直线分别与
轴,
轴相交于
,
两点,当点
运动时,求点
的轨迹方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91fe68ef3afaf1bce7999fdc2009ff6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4056761b8f826eeb6ad8c9a151d3c9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d252819147b54ea42ccb52c3668fb2f3.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若l过定点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fec0bc3a43265b63b6964476ca327fab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9f79d7939c88e9702962e5917cad290.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79ff575e55857af133edb24c8e61504f.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.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/d1f4f68b5c1be8c6b654641d442da766.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de52167e2e3f08cfd223a7d384b64755.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2934f18360c3569506de188b2307cf0d.png)
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名校
5 . 已知函数
,
(1)讨论
的单调性;
(2)若
存在两个零点![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
(ⅰ)求a的取值范围;
(ⅱ)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af2ee3664a4cd7fd377b23485fd14c83.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
(ⅰ)求a的取值范围;
(ⅱ)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc9d26d79e6a09476dc5a0d372c24867.png)
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7日内更新
|
106次组卷
|
2卷引用:广东省佛山市南海区第一中学2023-2024学年高二下学期阶段三暨期末统考模拟检测数学试题
名校
解题方法
6 . 已知函数
,若存在
恒成立,则称
是
的一个“上界函数”,如果函数
为
的一个“上界函数”.
(1)求实数
的取值范围;
(2)证明:若方程
有两个解
,则
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec6263576e5c3f2324a8dac311476bf9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e653994b245fbdc2ac3458429c65e69e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52ee140b690cece0721aa014811c3573.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)证明:若方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9587df831df1af5e7dd6be5fdc7bd8ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b725fdc8de9800f2692f6fea8585b1e9.png)
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7 . 数学中有很多相似的问题,
材料一:十七世纪法国数学家,被誉为业余数学家之王的皮埃尔·德·费马提出了一个著名的几何问题:“已知一个三角形,求作一点,使其与这个三角形的三个顶点的距离之和最小”,他的答案是:“当三角形的三个内角均小于
时,所求的点为三角形的正等角中心,即该点与三角形的三个顶点的连线两两成角
,当三角形有一内角大于或等于
时,所求点为三角形最大内角的顶点”,在费马问题中所求的点称为费马点.
材料二:布洛卡点,也叫“勃罗卡点”,定义为:已知
内一点
满足
,则称
为
的布洛卡点,
为
的布洛卡角,1875年,三角形的这一特殊点,被一个数学爱好者——法国军官布洛卡重新发现,并用他的名字命名.
已知
,
,
分别是
的内角
,
,
的对边,且
.
(1)求
;
(2)若
为
的费马点,且
,求
的值;
(3)若
为锐角三角形,
为
的布洛卡点,
为
的布洛卡角,证明:
.
材料一:十七世纪法国数学家,被誉为业余数学家之王的皮埃尔·德·费马提出了一个著名的几何问题:“已知一个三角形,求作一点,使其与这个三角形的三个顶点的距离之和最小”,他的答案是:“当三角形的三个内角均小于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00e4979100d4078609e253e2f99eed0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00e4979100d4078609e253e2f99eed0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00e4979100d4078609e253e2f99eed0b.png)
材料二:布洛卡点,也叫“勃罗卡点”,定义为:已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e428e7a09732be85c1224e9c8f6a71c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c25d734ea37934683320c146c2c67a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e428e7a09732be85c1224e9c8f6a71c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e428e7a09732be85c1224e9c8f6a71c5.png)
已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e428e7a09732be85c1224e9c8f6a71c5.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/481b91aa00df0bf153f717d87d1b12f7.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e428e7a09732be85c1224e9c8f6a71c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54728823efd2745d64ae9921f8807917.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1424f6ac5e01f56e2d486c68a5be1a0.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e428e7a09732be85c1224e9c8f6a71c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e428e7a09732be85c1224e9c8f6a71c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e428e7a09732be85c1224e9c8f6a71c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26f61d98c51b9f0344cf7b4562680f45.png)
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解题方法
8 . ①在高等数学中,关于极限的计算,常会用到:i)四则运算法则:如果
,
,则
,
,若B≠0,则
;ii)洛必达法则:若函数
,
的导函数分别为
,
,
,
,则
;
②设
,k是大于1的正整数,若函数
满足:对
,均有
成立,则称函数
为区间(0,a)上的k阶无穷递降函数.结合以上两个信息,回答下列问题;
(1)计算:①
;
②
;
(2)试判断
是否为区间
上的2阶无穷递降函数;并证明:
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac55b621b2f27bc851f91362ef8fed13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd7ae65af1a33cd09757bd180e607a22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37b0ca1f81ee531ffe24a41e094bf1d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4961ef8dba3a1376346c179290bfa545.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c8ff3cd9870608b67f0bc1d941162ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/090a91e4f3c8930674f98a9fa527709b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/783c88951a458d5862557f2a041f817a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46fd51a4ede3d8a6433cf0c114013956.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d16c5321133b0e626b32b5fa4b46181d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3900fe0b85ab5c057c4e3c2ceb0cb062.png)
②设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02a69e2c9a58ba833bd9912f3c14cdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67439f6be88350018cfba3f2aca73f06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(1)计算:①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7529d1357e6d9e2343b2bb7fcb9aaf55.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4e7be4d2e62ef20bcee0c65a3535879.png)
(2)试判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fff62e468bc81227b9586e769acbc5ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebbd5fbcb0ed2ac6d94982bc35a4f6b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/415e604884cb0c50cfcb95df9e9956e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2484f4dc493a45dae01bb8d385ee14e5.png)
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4卷引用:江苏省海门中学2023-2024学年高二下学期5月学情调研数学试卷
2024高三·全国·专题练习
解题方法
9 . 已知函数
.
(1)若函数
有三个零点分别为
,
,
,且
,
,求函数
的单调区间;
(2)若
,
,证明:函数
在区间
内一定有极值点;
(3)在(2)的条件下,若函数
的两个极值点之间的距离不小于
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/077315c5a7b12294497294e536831d77.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.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/291c25fc6a69d6d0ccfb8d839b9b4462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1f5cd91996571c9da95e6f26bc80661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23292eca257af6a97309ee40ce6cbf9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b37f19a2ad8f24cf63bff68be15faa67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/799f6009a476fa056e1af71f26dd2fd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b094cba781181aeb90752170e9ba6c94.png)
(3)在(2)的条件下,若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c6ce02259a85ea191541f4a708738f1.png)
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名校
解题方法
10 . 在平面直角坐标系中,点
在运动过程中,总满足关系式
.
(1)求点
的轨迹
的方程;
(2)过点
作两条斜率分别为
的直线
和
,分别与
交于
和
,线段
和
的中点分别为
,若
,证明直线
过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c62b58e1ce45cfd3fe723345eaf411f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17aa130296d594a23b0a7a864fc33320.png)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd3b260036958c271fee22820b05fdb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4f5fac15de56be6dfb7ba2429b54cea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d762c4e0c2e788c94066aeea1530f4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/227c1d105f7abf228e7a4f3097ae93f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2026c8a047f60c7b84f4078466dcce6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/077aaf808a6243d4af30a3eb9320fb99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42887d9bf31c1dd99f13c39e63c9ab9.png)
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4卷引用:河南省驻马店市新蔡县第一高级中学2023-2024学年高二下学期6月月考数学试题