定义:有一组对角是直角的四边形叫做“准矩形”;有两组邻边(不重复)相等的四边形叫做“准菱形”.如图①,在四边形ABCD中,若∠A=∠C=90°,则四边形ABCD是“准矩形”;如图②,在四边形ABCD中,若AB=AD,BC=DC,则四边形ABCD是“准菱形”.
![](https://img.xkw.com/dksih/QBM/2020/5/19/2466210493464576/2467367062355968/STEM/5b00ac8e-023e-49c6-9b99-225431c59c63.png?resizew=404)
(1)如图,在边长为1的正方形网格中,A、B、C在格点(小正方形的顶点)上,请分别在图③、图④中画出“准矩形”ABCD和“准菱形”ABCD′.(要求:D、D′在格点上);
![](https://img.xkw.com/dksih/QBM/2020/5/19/2466210493464576/2467367062355968/STEM/6dd12ea9-030c-4ea0-beb6-3a28d1a8e53e.png?resizew=421)
(2)下列说法正确的有 ;(填写所有正确结论的序号)
①一组对边平行的“准矩形”是矩形;②一组对边相等的“准矩形”是矩形;
③一组对边相等的“准菱形”是菱形;④一组对边平行的“准菱形”是菱形.
(3)如图⑤,在△ABC中,∠ABC=90°,以AC为一边向外作“准菱形”ACEF,且AC=EC,AF=EF,AE、CF交于点D.
①若∠ACE=∠AFE,求证:“准菱形”ACEF是菱形;
②在①的条件下,连接BD,若BD=
,∠ACB=15°,∠ACD=30°,请直接写出四边形ACEF的面积.
![](https://img.xkw.com/dksih/QBM/2020/5/19/2466210493464576/2467367062355968/STEM/5b00ac8e-023e-49c6-9b99-225431c59c63.png?resizew=404)
(1)如图,在边长为1的正方形网格中,A、B、C在格点(小正方形的顶点)上,请分别在图③、图④中画出“准矩形”ABCD和“准菱形”ABCD′.(要求:D、D′在格点上);
![](https://img.xkw.com/dksih/QBM/2020/5/19/2466210493464576/2467367062355968/STEM/6dd12ea9-030c-4ea0-beb6-3a28d1a8e53e.png?resizew=421)
(2)下列说法正确的有 ;(填写所有正确结论的序号)
①一组对边平行的“准矩形”是矩形;②一组对边相等的“准矩形”是矩形;
③一组对边相等的“准菱形”是菱形;④一组对边平行的“准菱形”是菱形.
(3)如图⑤,在△ABC中,∠ABC=90°,以AC为一边向外作“准菱形”ACEF,且AC=EC,AF=EF,AE、CF交于点D.
①若∠ACE=∠AFE,求证:“准菱形”ACEF是菱形;
②在①的条件下,连接BD,若BD=
![](https://img.xkw.com/dksih/QBM/2020/5/19/2466210493464576/2467367062355968/STEM/f13a21b1e451489698c3e72b915a1017.png?resizew=17)
![](https://img.xkw.com/dksih/QBM/2020/5/19/2466210493464576/2467367062355968/STEM/62dcce38-ef6f-4468-846b-a89512cdcc7d.png?resizew=140)
19-20八年级下·江苏南京·期中 查看更多[10]
江苏省南京市栖霞区2019-2020学年八年级下学期期中数学试题江苏省南京市联合体2019-2020学年八年级下学期期中数学试题山东省青岛三十九中2021-2022学年九年级上学期第一次月考数学试题江苏省泰州市姜堰区四校联考2021-2022学年八年级下学期第一次月考数学试题江苏省南京市六合区励志学校2021-2022学年八年级下学期4月月考数学试题江苏省盐城市滨海县第一初级中学教育集团2022-2023学年八年级下学期第一次月考数学试卷浙江省宁波市镇海区镇海区立人中学2022-2023学年八年级下学期期中数学试题江苏省盐城市滨海县滨淮教育集团2022-2023学年八年级下学期第二次学情检测数学试题湖北省鄂州市梁子湖区2022-2023学年八年级下学期期中数学试题江苏省南京师范大学附属中学江宁分校2023-2024学年八年级下学期数学阶段练习题(3月20日)
更新时间:2020-05-21 10:14:03
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名校
【推荐1】已知
,点
为
中点,
,
为边
,
上的动点,且满足
,
为平面内一点,
,
,连接
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/5/8dd024da-d33f-4fa7-a8cd-12be1aae1fe1.png?resizew=323)
(1)若点
为
边
和边
上的高的交点,求证:
;
(2)若点
不与三角形高的交点重合,
与
是否还有上述关系?请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7faabc484ce3666706c1beffda4bcfe2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90dfb0a85bb6aee4a1d8fc1abad4eecb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/385b11357932bd24e9e16e95aacd3cdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06e322e0c87479bba874db9ae9ba36b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abf80148409afb32ced0b4f59f1ba709.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/5/8dd024da-d33f-4fa7-a8cd-12be1aae1fe1.png?resizew=323)
(1)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ac64951c922a53961cb19bb47ace476.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5af342d3b871ace448ccc7c648528288.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d890499dca9a8ef30addafe41d6e771.png)
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【推荐2】课本再现
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/29/5706b251-8aa9-44f8-b917-969c21a10b16.png?resizew=385)
(1)定理证明:为了证明该定理,小明同学画出了图形(如图1),并写出了“已知”和“求证”,请你完成证明过程,
已知:在
中,对角线
.
求证:
是矩形.
(2)知识应用:如图2,在
中,对角线
和
相交于点O,
是等边三角形,
.
①求证:
是矩形;
②延长
至点E,连接
交
于点F,若
,求
的值.
思考 我们知道,矩形的对角线相等,反过来,对角线相等的平行四边形是矩形吗? 可以发现并证明矩形的一个判定定理:; 对角线相等的平行四边形是矩形. |
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/29/5706b251-8aa9-44f8-b917-969c21a10b16.png?resizew=385)
(1)定理证明:为了证明该定理,小明同学画出了图形(如图1),并写出了“已知”和“求证”,请你完成证明过程,
已知:在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5138a9f70d5e8b0580e30fef6eb7baef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01476dfb5970e27f54f742c27b9515f9.png)
求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5138a9f70d5e8b0580e30fef6eb7baef.png)
(2)知识应用:如图2,在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5138a9f70d5e8b0580e30fef6eb7baef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2b83beedb3438153e6f728545fe3e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76d527d4795ece4a5756d1cf8dba31e1.png)
①求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5138a9f70d5e8b0580e30fef6eb7baef.png)
②延长
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a299d2b999568e80be8005565ba209a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
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【推荐1】定义一种变换:平移抛物线
得到抛物线
,使
经过
的顶点
.设
的对称轴分别交
于点
,点
是点
关于直线
的对称点.
![](https://img.xkw.com/dksih/QBM/2016/4/19/1574194110226432/1574194115944448/STEM/f56a5864419649359632a6f51dd8fd1c.png)
(1)如图1,若
:
,经过变换后,得到
:
,点
的坐标为
,则①
的值等于______________;
②四边形
为( )
(2)如图2,若
:
,经过变换后,点
的坐标为
,求
的面积;
(3)如图3,若
:
,经过变换后,
,点
是直线
上的动点,求点
到点
的距离和到直线
的距离之和的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://img.xkw.com/dksih/QBM/2016/4/19/1574194110226432/1574194115944448/STEM/f56a5864419649359632a6f51dd8fd1c.png)
(1)如图1,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/344ccbf79da6ad7e3709d6fa72efb756.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99b085858362045208caf3dd60121256.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
②四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
A.平行四边形 | B.矩形 | C.菱形 | D.正方形 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3666050060fb25232784bb8ed3545ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/549be91a5df0e35bd1b893f1c1a0c919.png)
(3)如图3,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4441b4a277984abf44b51c087d0d3d10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e1f4f255d191786f7d330d278868c2d.png)
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【推荐2】如图,在平行四边形ABCD中,以点A为圆心,AB长为半径画弧交AD于点F,再分别以点B,F为圆心,大于
的长为半径画弧,两弧交于一点P,连接AP并延长交BC于点E,连接EF.
(1)求证:四边形ABEF是菱形.
(2)设AE与BF相交于点O,四边形ABEF的周长为16,BF=4,求AE的长和∠C的度数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36657d9f8560180cbda94326e8a9cf53.png)
(1)求证:四边形ABEF是菱形.
(2)设AE与BF相交于点O,四边形ABEF的周长为16,BF=4,求AE的长和∠C的度数.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/10/04212220-79b9-48f2-8acb-bcd5097bd99f.png?resizew=193)
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【推荐1】在一次数学探究活动中,王老师设计了一份活动单:
“神州”学习小组通过操作、观察、讨论后汇报:点
的位置不唯一,它在以
为弦的圆弧上(点
、
除外),…小乐同学画出了符合要求的一条圆弧(如图1).
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/3/1077e408-8027-407a-83f7-042f16691441.png?resizew=283)
(1)小乐同学提出了下列问题,请你帮助解决.
①该弧所在圆的半径长为___________;
②
面积的最大值为___________;
(2)经过比对发现,小明同学所画的角的顶点不在小华所画的圆弧上,而在如图1所示的弓形外部,我们记为
,请你利用图1证明
.
(3)请你运用所学知识,结合以上活动经验,解决问题:如图2,已知矩形
的边长
,
,点
在直线
的右侧,且
,则线段
长的最大值为___________.
已知线段![]() ![]() 尝试操作后思考:这样的点 ![]() ![]() |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/3/1077e408-8027-407a-83f7-042f16691441.png?resizew=283)
(1)小乐同学提出了下列问题,请你帮助解决.
①该弧所在圆的半径长为___________;
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(2)经过比对发现,小明同学所画的角的顶点不在小华所画的圆弧上,而在如图1所示的弓形外部,我们记为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c314398e26ffc7164b82946eeb4273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f201ec8536c5723598cd3741f380f9.png)
(3)请你运用所学知识,结合以上活动经验,解决问题:如图2,已知矩形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7bae5203f4b4acf23779114b3466e17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65a3e478bb87d094e3a0af30dd10ae8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63247af194edc9d72cd3ca7365a5d128.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
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【推荐2】如图1,
是
的直径,
是
的弦,
的平分线
交
于点B,交
于M,连接
、
.
(1)证明:
.
(2)填空:(直接将结果写在相应的横线上)
,
,
.
(3)如图2,过点D作
,垂足为N,若
,求
的值.
(4)记
,
,试用含m,n的式子表示
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3981e7286d41960daf4e110c1c84e03a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d97dc3b752832906de41447bb58a341.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b1bd1adfe4cc6566218f19970c2fd3b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/26/5b4c42ec-a198-4c6d-94ce-6d1aa0ff1dd2.png?resizew=510)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f81e24376a13d648c2ed0dc73bc710e.png)
(2)填空:(直接将结果写在相应的横线上)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dbd7c178ea9a3515024c3ed9d64e225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7472d84d0ff25e8a58a48499b661c93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eca750aa9196c9e5f3e55fb5d0c070f1.png)
(3)如图2,过点D作
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f22a601861b2d7c266c307e4ae05784.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db9e3dada9ebe405b873f7d632b65b36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/defdf69f0eb7e573b976a9b9d8027e79.png)
(4)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f054eb8c5f5cb49310f8e76699a58aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34293b0e5b0ccd82aaf2197561865efc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28bde380807790b7d731aa2aaa14f92d.png)
您最近一年使用:0次
解答题-问答题
|
较难
(0.4)
【推荐1】如图1,二次函数
的图象交x轴于点A、B,其中点B的坐标为(2,0),点C的坐标为(0,2),过点A、C的直线交二次函数的图象于点D.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/23/8b1e4e47-8772-43cc-a9c4-9b3f46863bc5.png?resizew=704)
(1)求二次函数和直线
的函数表达式;
(2)连接
,求
的面积;
(3)在y轴上是否存在一点Q,使得
,若存在求出点Q的坐标,若不存在,请说明理由;
(4)如图2,点P为直线
上在第一象限内的动点,连接
,将
沿
翻折得到
,连接
,当
为直角三角形时,直接写出点P的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43029dfd2a2b47b764679b92dab02259.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/23/8b1e4e47-8772-43cc-a9c4-9b3f46863bc5.png?resizew=704)
(1)求二次函数和直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
(2)连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d97dc3b752832906de41447bb58a341.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd4c625a55ef1d2920a0605d52c8da23.png)
(3)在y轴上是否存在一点Q,使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2d2a276f84a34bdfb378c68855ac26e.png)
(4)如图2,点P为直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/025959c2e20acf2e364e9684c684e005.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c025ee3317be1099b7bf03a11e37ed4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b6accdd9b317c922d335e44911df357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cff7399ecc698e2fb415147c96d0d03.png)
您最近一年使用:0次
解答题-问答题
|
较难
(0.4)
解题方法
【推荐2】如图,⊙O的直径
,点
为弧
上一点,连接
、
,点
为劣弧
上一点(点
不与点
、
重合),连接
交
、
于点
、
.
![](https://img.xkw.com/dksih/QBM/2021/5/2/2712454031933440/2718091199709184/STEM/bef00498-fb3c-4a94-9311-abef5373dd54.png?resizew=199)
![](https://img.xkw.com/dksih/QBM/2021/5/2/2712454031933440/2718091199709184/STEM/3449fd4c-a045-4405-9c8f-0c01a75233c1.png?resizew=197)
(1)当
时,
的长度为______;
(2)当点
为劣弧
的中点,且
∽
时,求
的度数;
(3)当
,且
为直角三角形时,求四边形
的面积(直接写出结果).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef49a3ca580a144cc65a609c167facc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.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/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef49a3ca580a144cc65a609c167facc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://img.xkw.com/dksih/QBM/2021/5/2/2712454031933440/2718091199709184/STEM/bef00498-fb3c-4a94-9311-abef5373dd54.png?resizew=199)
![](https://img.xkw.com/dksih/QBM/2021/5/2/2712454031933440/2718091199709184/STEM/3449fd4c-a045-4405-9c8f-0c01a75233c1.png?resizew=197)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8a25a10398bdb8bacde724aa584ff68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
(2)当点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2b4dcc093218443f71a046b6df94bbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028c33f1a5112a4e4cce0f0cb6a7cc3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d39b8d91afc34e4a9b0fdbb6bafb9087.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d158fc1e5e3ce232e3ee2328c877dffe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d0cbf8d91c8197cb3ac9b2ddcc62daf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c87ec29df8f8378b197102c50a6c0e3.png)
您最近一年使用:0次