1 . 判断正误,正确的写“正确”,错误的写“错误”.
(1)若两直线相交,则交点坐标一定是两直线方程所组成的二元一次方程组的解.( )
(2)无论m为何值,
与
必相交.( )
(3)若两直线的方程组成的方程组有解,则两直线相交.( )
(4)点
和点
之间的距离为
.( )
(5)在两点间的距离公式中
与
,
与
的位置可以互换,不影响计算结果.( )
(1)若两直线相交,则交点坐标一定是两直线方程所组成的二元一次方程组的解.
(2)无论m为何值,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b979396a703fb14715ba39232f5786a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a09ee5220b905b6cadccbe09100fb25.png)
(3)若两直线的方程组成的方程组有解,则两直线相交.
(4)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3acbcf5ca270d1b5edd8982bc8d590c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af13e3c26639ac539f13f559b74a0cce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9f2416d1f75a45a314331146550832e.png)
(5)在两点间的距离公式中
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46f6872ffb1934339c53c2c2282d5889.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54015ff5b49e3283901da1291b6b921d.png)
您最近一年使用:0次
2 . 如果两个圆的方程组成的方程组只有一组实数解,则两圆外切.( )
您最近一年使用:0次
3 . 思维辨析(对的写正确,错误的写错误)
(1)若点
在直线
上,则
.( )
(2)若两直线的方程组成的方程组有解,则两直线相交.( )
(3)若两直线相交,则交点坐标一定是两直线方程所组成的二元一次方程组的解.( )
(4)若直线
与直线
的交点为
,则
.( )
(1)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf5a6145990adf5574f0e0f2fc828ea4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1773ec03a4c0da31eeb6484f84f2634e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46a70d32c64918aa4d1d9d3ce0bdbf7b.png)
(2)若两直线的方程组成的方程组有解,则两直线相交.
(3)若两直线相交,则交点坐标一定是两直线方程所组成的二元一次方程组的解.
(4)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9231260a2de7949154b7244bf70785c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09324568f2f3995b2f932e66ee5926ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4562f3225c98cf5cb11b47d98c9cc9c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2feac7a3eaffd79d927bad4a572b5173.png)
您最近一年使用:0次
名校
4 . 已知点
和直线
,则点
到直线
的距离证明可用公式
计算.
例如:求点
到直线
的距离.
解:
直线
,其中
,
.
点
到直线
的距离为:
.
根据以上材料,解答下列问题:
(1)求点
到直线
的距离;
(2)已知⊙
的圆心
坐标为
,半径
为
,判断⊙
与直线
的位置关系,并说明理由:
(3)已知直线
与
平行,求这两条直线之间的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7775aa57ca0e62216f3039ed88dceed0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c15fb18163df0690365a0d2e7ee88f5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c15fb18163df0690365a0d2e7ee88f5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0682ce7c7d01d65347c659227e6c3e15.png)
例如:求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a42451bdbef6c82dbaf8e06f0614794.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/960c22d0509ff3a0d4620afe187b196a.png)
解:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16f3d198e76391779fa3badc848c8ac8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/960c22d0509ff3a0d4620afe187b196a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/367e788c32187ae2cc97aaa24da1d40d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ab1c19b66cda3fb899f06d9a25e973c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2de0d10ef8b748d4531250c37c5d3f9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a42451bdbef6c82dbaf8e06f0614794.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/960c22d0509ff3a0d4620afe187b196a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46ed48c24e5697d14fe19abf3586fa6f.png)
根据以上材料,解答下列问题:
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c2f21b1baf0624482fd41d7ba390341.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e235d7dd12f948f5ffb2e5afddc95612.png)
(2)已知⊙
![](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/fb0e705301752424a492f6277ed7774e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5627cec233ab4cd6ea8a864e220a6946.png)
(3)已知直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1d7df623642896d720d6956ed1f0ff6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a515853c22f0145b36c512079134dd5.png)
您最近一年使用:0次
5 . 我国古代数学著作《九章算术》中记载:斜解立方,得两堑堵.其意思是:一个长方体沿对角面一分为二,得到两个一模一样的堑堵.如图,在长方体
中,
,
,
,将长方体
沿平面
一分为二,得到堑堵
,下列结论正确的序号为______ .
①点C到平面
的距离等于
;
②
与平面
所成角的正弦值为
;
③堑堵
外接球的表面积为
;
④堑堵
没有内切球.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efc6e4b936d7a800e839a30c3839574d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65a3e478bb87d094e3a0af30dd10ae8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f3e58edd1f900ca82bb2a3058293f52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/679748eab882a6be0fefd2cc300349a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b5b14d74bdf9ed7c45b2e754b7ccc4f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/2/203cf047-3c7e-43ff-9a8e-fb0157d5f7d4.png?resizew=233)
①点C到平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/679748eab882a6be0fefd2cc300349a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81365a3726621b6557bd26f3a1a51cae.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/588eb9393564a33552c4b2e8de837ca5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a24acb11fac4bcf6a86e3e9223a48b.png)
③堑堵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b5b14d74bdf9ed7c45b2e754b7ccc4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f08a01aed02ce1eaf1aaefaa0342b7ad.png)
④堑堵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b5b14d74bdf9ed7c45b2e754b7ccc4f.png)
您最近一年使用:0次
6 . 《九章算术·商功》:“斜解立方,得两壍堵(qiàn dǔ).斜解壍堵,其一为阳马,一为鳖臑(biē nào).阳马居二,鳖臑居一,不易之率也.”文中所述可用下图表示:
![](https://img.xkw.com/dksih/QBM/2022/1/14/2894203289747456/2895176848777216/STEM/8c0d64b8-e798-4905-a031-747276d8fa23.png?resizew=384)
则几何体“鳖臑”的四个面中,直角三角形的个数为_______ ;若上图中的“立方”是棱长为1的正方体,则
的中点到直线
的距离等于________ .
![](https://img.xkw.com/dksih/QBM/2022/1/14/2894203289747456/2895176848777216/STEM/8c0d64b8-e798-4905-a031-747276d8fa23.png?resizew=384)
则几何体“鳖臑”的四个面中,直角三角形的个数为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e539f26ed5e0b20ff7220559324869a4.png)
您最近一年使用:0次
名校
解题方法
7 . 《九章算术·商功》:“斜解立方,得两堑堵.斜解堑堵,其一为阳马,一为鳖臑.阳马居二,鳖臑居一,不易之率也.合两鳖臑三而一,验之以棊,其形露矣.”刘徽注:“此术臑者,背节也,或曰半阳马,其形有似鳖肘,故以名云.中破阳马,得两鳖臑,鳖臑之起数,数同而实据半,故云六而一即得.”
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/27/e5993170-2f4e-4cc5-b942-25e82698d51b.png?resizew=444)
如图,在鳖臑ABCD中,侧棱
底面BCD;
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/27/a607565f-9b51-4909-854f-36d57edfe0e2.png?resizew=340)
(1)若
,
,
,
,求证:
;
(2)若
,
,
,试求异面直线AC与BD所成角的余弦.
(3)若
,
,点P在棱AC上运动.试求
面积的最小值.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/27/e5993170-2f4e-4cc5-b942-25e82698d51b.png?resizew=444)
如图,在鳖臑ABCD中,侧棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f9157fce2a8339d281178c7c0bccbe.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/27/a607565f-9b51-4909-854f-36d57edfe0e2.png?resizew=340)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bd6a2b112facda441f4e34bf5c145fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00be7c72b7d222730571ce5d7c288eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c125d80008eed00b5bf47dc5df47246.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e468b7ccc9795b5feb53ad072e597b34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78f2b8dcbb2f7c2047896bc7aecc22bf.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0402dd5ae3db10281f9f1e11738bcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/037b342a682cbd4241855a243da3c016.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff9c7cbcc38b28d45c8539710e5b260a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2e1ab67f8e48ad3340cf9d165cd75f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acee03d4bb4667b6c345221b6c9b0fa4.png)
您最近一年使用:0次
8 . (1)求一个棱长为
的正四面体的体积,有如下未完成的解法,请你将它补充完成.解:构造一个棱长为1的正方体—我们称之为该四面体的“生成正方体”,如左下图:则四面体
为棱长是___________的正四面体,且有
___________.
![](https://img.xkw.com/dksih/QBM/2021/5/3/2712963070132224/2799670116392960/STEM/b3a43d08-3809-4282-8b2f-46b52950fd10.png?resizew=380)
(2)模仿(1),对一个已知四面体,构造它的“生成平行六面体”,记两者的体积依次为
和
,试给出这两个体积之间的一个关系式,不必证明;
(3)如1图,一个相对棱长都相等的四面体(通常称之为等腰四面体),其三组棱长分别为
,
,
,类比(1)(2)中的方法或结论,求此四面体的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68ac02c2f91cadb1e328bc6ab9b9c491.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dafefd79de97043ba8a070428467e285.png)
![](https://img.xkw.com/dksih/QBM/2021/5/3/2712963070132224/2799670116392960/STEM/b3a43d08-3809-4282-8b2f-46b52950fd10.png?resizew=380)
(2)模仿(1),对一个已知四面体,构造它的“生成平行六面体”,记两者的体积依次为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6cefccb97d4ec7d785b9db04ea196a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f37c08f1fd1b7f1d7a1052b9fd8c60e.png)
(3)如1图,一个相对棱长都相等的四面体(通常称之为等腰四面体),其三组棱长分别为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2967337e3fcb228dded64ab0c41a17e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50690dab38f4512eb72e18b7f86cf6f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4056761b8f826eeb6ad8c9a151d3c9c.png)
您最近一年使用:0次
2021-09-02更新
|
407次组卷
|
6卷引用:上海市复旦大学附属中学2020-2021学年高二下学期期中数学试题
上海市复旦大学附属中学2020-2021学年高二下学期期中数学试题(已下线)8.3简单几何体的表面积与体积C卷沪教版(2020) 必修第三册 同步跟踪练习 第11章 11.3.1 多面体(已下线)第02讲 简单几何体(核心考点讲与练)(2)(已下线)11.3 多面体与旋转体(作业)(夯实基础+能力提升)-【教材配套课件+作业】2022-2023学年高二数学精品教学课件(沪教版2020必修第三册)(已下线)专题08多面体与旋转体(2个知识点3种题型1种高考考法)-【倍速学习法】2023-2024学年高二数学核心知识点与常见题型通关讲解练(沪教版2020必修第三册)
名校
9 . 国家主席习近平指出:中国优秀传统文化有着丰富的哲学思想、人文精神、教化思想、道德理念等,可以为人们认识和改造世界提供有益启迪.我们要善于把弘扬优秀传统文化和发展现实文化有机统一起来,在继承中发展,在发展中继承.《九章算术》作为中国古代数学专著之一,在其“商功”篇内记载:“斜解立方,得两壍堵.斜解壍堵,其一为阳马,一为鳖臑”.刘徽注解为:“此术臑者,背节也,或曰半阳马,其形有似鳖肘,故以名云”.鳖臑,是我国古代数学对四个面均为直角三角形的四面体的统称.在四面体
中,
平面
.
![](https://img.xkw.com/dksih/QBM/2021/7/9/2760356260454400/2761304616468480/STEM/acdd4b31b8504295b1d47e95e3567ddf.png?resizew=455)
(1)如图1,若
、
、
分别是
、
、
三边的的中点,
在
上,且
,求证:
平面
;
(2)如图2,若
,垂足为
,且
,
,
,求直线
与平面
所成角的大小;
(3)如图2,若平面
平面
,求证:四面体
为鳖臑.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9e1bf2cc650448488a19c6301125b31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cf468f5132e14ee1d8cc766808b11af.png)
![](https://img.xkw.com/dksih/QBM/2021/7/9/2760356260454400/2761304616468480/STEM/acdd4b31b8504295b1d47e95e3567ddf.png?resizew=455)
(1)如图1,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.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/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dec0d25fa88ea9f0b003b83b7e2fe88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f28f9f503c0a023ed7e78e48123cc95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)如图2,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d900531973c546625694146fa1509ab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/618c5704137191d21172232bdb26b4d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68b40d0d2f3cdd8981bb792ad87efb42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71807a35b3170fce28ee6edf4c00d083.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf4c26f3f4d96117f087400a0f32ece8.png)
(3)如图2,若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1095b030f441de5fb223781b00f3dd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aeb5255e2159617505e0c87d01437a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9e1bf2cc650448488a19c6301125b31.png)
您最近一年使用:0次
2021-07-10更新
|
392次组卷
|
2卷引用:四川省成都市第七中学2020-2021学年高一下学期期末考试数学试题
名校
10 . 随着社会的进步,人民的生活水平逐步提高,金秋时节.公园鲜花盛开,为了让市民有更好地赏花体验,公园开辟出一块
区域用作花卉展示,
,如图所示,以
为坐标原点,建立直角坐标系,弧
是圆
的一部分,圆上的动点
满足到两定点
的距离之比等于
,曲边图形
作为主展区(Ⅰ),梯形
作为副展区(Ⅱ).
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/19/b495f73a-9725-432d-bb2a-0c8c4678508b.png?resizew=157)
(1)求圆
的轨迹方程,并计算主展区(Ⅰ)曲边图形
的面积;
(2)若弧
上的点到线段
的最短距离是1,求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90141f4c399bcf7dbffaedd91ee66eb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/334528b4f29f9301875430197753b630.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42887d9bf31c1dd99f13c39e63c9ab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38f23bd7203e1578c9f5249b4fc5f26b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eac97e6740365c85ad857aff85cefbe5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7b4bbd23b2a1ffba33f2bec1495653a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fa7bbd7831e9ff4f8cffc8889d34f05.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/19/b495f73a-9725-432d-bb2a-0c8c4678508b.png?resizew=157)
(1)求圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7b4bbd23b2a1ffba33f2bec1495653a.png)
(2)若弧
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42887d9bf31c1dd99f13c39e63c9ab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
您最近一年使用:0次
2021-11-23更新
|
81次组卷
|
2卷引用:山西省怀仁市第一中学2021-2022学年高二上学期期中数学(理)试题