1 . 【阅读材料】:
解方程:
时,先两边同乘以x,得
,解之得
,
,经检验无增根,所以原方程的解为
,
.
【模仿练习】
(1)解方程
;
【拓展应用】
(2)如图1,等腰直角
的直角顶点
的坐标为
,B,C两点在反比例函数
的图象上,点
的坐标是
,且
,求
的值;
有
,
两点,如果
,
,那么
是否为定值,若存在请求出,不存在请说明理由.
解方程:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87ea5965fd560110681de04037f87d0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e14a43d7dd192b3eff3770ecd36e61e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de10eb4cf291d00db3bb92596143afa1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7eba583e37243f3ba166bd1c11e58498.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de10eb4cf291d00db3bb92596143afa1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7eba583e37243f3ba166bd1c11e58498.png)
【模仿练习】
(1)解方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3463be5bec22bc07fb52810c6087736b.png)
【拓展应用】
(2)如图1,等腰直角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/623afc24f2227004b0e1b3922dfb954b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/498bcfd1aac03057dcd0adef2dd113a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8ed892caba869acd1e610c38815cf65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de8610232c77741a37463feba1a66c94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b0b612460326448de36e160c8d29af9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b27fe9b99349c9b4742daa56ab7db85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e207dc5f468b23c84db05c227bed974.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6417bed1269505442c0756b8b44bcb81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59787c78163fde07da77755b07b3053f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29d19f98faf2f4b730c5c838e44b0331.png)
您最近一年使用:0次
真题
名校
2 . 小亮在学习中遇到这样一个问题:
小亮分析发现,此问题很难通过常规的推理计算彻底解决,于是尝试结合学习函数的经验研究此问题,请将下面的探究过程补充完整:
根据点
在弧
上的不同位置,画出相应的图形,测量线段
的长度,得到下表的几组对应值.
![](https://img.xkw.com/dksih/QBM/2020/7/16/2507276540919808/2507740623167488/STEM/b9b1be0c9f7e4bf98668516d0c1ae29e.png?resizew=650)
操作中发现:
①"当点
为弧
的中点时,
".则上中
的值是
②"线段
的长度无需测量即可得到".请简要说明理由;
将线段
的长度作为自变量
和
的长度都是
的函数,分别记为
和
,并在平面直角坐标系
中画出了函数
的图象,如图所示.请在同一坐标系中画出函数
的图象;
继续在同一坐标系中画出所需的函数图象,并结合图象直接写出:当
为等腰三角形时,线段
长度的近似值.(结果保留一位小数).
如图,点![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1baca09215d12421a58bd6a48ae16c35.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/364017d72ccd8d2094e3bbd11943cb62.png)
![](https://img.xkw.com/dksih/QBM/2020/7/16/2507276540919808/2507740623167488/STEM/b9b1be0c9f7e4bf98668516d0c1ae29e.png?resizew=650)
操作中发现:
①"当点
![](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/057e4faff539152829d03a85051b178d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
②"线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac0c12379ff58d8ddf66547d7a873baf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f0105ace7af30408d4efa2f59031c6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00bab17635a999236e8d2e35017a208d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73a69a04d681f4400acbfdebe236e75a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1b086c3a585c988429acb497ce9fe02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1b086c3a585c988429acb497ce9fe02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73a69a04d681f4400acbfdebe236e75a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a416e351c08669214734418cf60209e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b6fdadad5411ba41fae9277326f49cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/1/fd75576c-5d61-45c7-90da-88bfd7b88a8a.png?resizew=241)
您最近一年使用:0次
2020-07-17更新
|
1644次组卷
|
11卷引用:2021年广东省东莞市中考一模数学试题
2021年广东省东莞市中考一模数学试题河南省2020年中考数学试题(已下线)必刷卷02-2021年中考数学考前信息必刷卷(江苏无锡专用)(已下线)【万唯原创】2021年安徽省试题研究-全国视野推荐题型1(已下线)【万唯原创】2021年广东省试题研究-讲册-第三部分 创新题型2(已下线)【万唯原创】2021年山西省面对面-讲册第二部分-专题八 3(已下线)【万唯原创】2021年河南试题研究-第二部分题型7类型1+2(已下线)【万唯原创】2021年河南省面对面-专题练-专题12(已下线)【万唯原创】2021年山西专项集训-解答题专项-第二部分题型4+5(已下线)【万唯原创】2021年广东试题研究-讲册第三部分 创新题型北京市首都师范大学附属中学2021-2022下学期九年级下学期3月月考数学试题
3 . 在
中,
,点D是边
上一点,过点D作
于点E,点F是边
的延长线上一点,且
,连接
,设
两点间的距离为
两点间的距离为
两点间的距离为
.
根据学习函数的经验,我们对因变量随自变量x的变化而变化的规律来进行探究.
(1)列表:下表的已知数据是根据
两点间的距离x进行取点、画图、测量,分别得到的几组对应值:
请你通过计算补全表格:
______;
(2)描点、连线:在平面直角坐标系
中,描出表中各组数值所对应的点
,并画出函数
关于x的图象、函数
关于x的图象;
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/29/5f447c97-dc4e-4899-b3b5-6e0849f1ca43.png?resizew=374)
(3)探究性质:请写出一条
关于x的函数的性质:_________;
(4)解决问题:当
是等腰三角形时,x大约是______
(结果保留一位小数).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f8f88798ec42a58dccd212586382b23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/184874f89463068ebc7c9baf851ee206.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68fbbd17c89f03dbb61cd6ffdb9a0344.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b1bd1adfe4cc6566218f19970c2fd3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78bc939ef2208ac7c9c07b2cca587abd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dca8a2ccce217c5cef108c19d92b1326.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aa69fd8445d01c98634c2e885b47d5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d8259fb02e85ad9f11c9e750ac4a903.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8dc7001bf6c904ee2528e22c3de26241.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3085f96c87b66a354ff38ce3b64dcfbd.png)
根据学习函数的经验,我们对因变量随自变量x的变化而变化的规律来进行探究.
(1)列表:下表的已知数据是根据
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aa69fd8445d01c98634c2e885b47d5a.png)
![]() | 0 | 0.25 | 0.5 | 0.75 | 1 | 1.25 | 1.5 | 1.75 | 2 | 2.25 | 2.5 | 2.75 | 3 |
![]() | 4 | 4.01 | 4.02 | 4.03 | 4.05 | 4.10 | 4.16 | 4.24 | 4.33 | 4.45 | 4.61 | 4.78 | a |
![]() | 3 | 3.07 | 3.17 | 3.27 | 3.37 | 3.54 | 3.70 | 3.88 | 4.08 | 4.29 | 4.55 | 4.82 | 5.11 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
(2)描点、连线:在平面直角坐标系
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63182f620ffd33adcef47bcac31b59a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/524abb4156c79c2c1c69ce3d2d090ff0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c6c18e0a00b092e3119f03bbb85ec3b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/29/5f447c97-dc4e-4899-b3b5-6e0849f1ca43.png?resizew=374)
(3)探究性质:请写出一条
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/524abb4156c79c2c1c69ce3d2d090ff0.png)
(4)解决问题:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c105d6ba18fbb0581fb982175e2eac9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9efa9fbcfb9595e2f031aa691db4564b.png)
您最近一年使用:0次
4 . 已知:如图,
中,
,
,点
,点
,反比例函数
的图象经过点A.
(1)求反比例函数的解析式;
(2)设直线
的解析式为
.
①直接写出不等式
的解集;
②将直线
向上平移m个单位后经过反比例函数
图象上的点
求m,n的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd967903ed5a6f640a5b801ec8be0070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed10df4140819d5451773a45de66201b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b10134e7a46e6f6f7cb9d5e2371727d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6fbd364e946281349dbe112a0a14dea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae2186d147376d88c991d9b7308f1ce4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa915a60a2d6e535369715ba84015b4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/25/603702d5-665a-4b54-a0ca-7b7346185af1.png?resizew=171)
(1)求反比例函数的解析式;
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/766bc42b7ead98238a339bb4dc42bb51.png)
①直接写出不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/497a2b870e8c38105958ccb8e1091667.png)
②将直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa915a60a2d6e535369715ba84015b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6529806497d2e4fb3d0c150993cfa12b.png)
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5 . 如图,在形OAB中,
,C是半径BO上一动点,过点B作AC的垂线交线段AC的延长线于点D,交线段AO的延长线于点E,连接DO.明明发现,随着点C位置的改变,
的三边都随之改变,所以,明明决定以BC的长度为自变量,设BC的长为
,借助学习函数的经验来研究
三边的变化规律,请你将下面的探究过程补充完整.
![](https://img.xkw.com/dksih/QBM/2021/5/17/2723067266187264/2781382295035904/STEM/5e730894-e028-4d85-b4fb-257696e4357f.png)
(1)根据点C在OB上的不同位置,画出相应的图形,测量线段OD,DE的长度,得到下表的几组对应值.
①上表中a的值为___________;
②OE与自变量BC的长度具有某种关系,所以无需测量OE,通过推理并计算可以得到,请说明理由.
(2)在同一平面直角坐标系
中,以BC的长为x,OD的长为
,DE的长为
,如图,已经画出了
的函数图象,请你描点并画出
的函数图象.
![](https://img.xkw.com/dksih/QBM/2021/5/17/2723067266187264/2781382295035904/STEM/156fcfe7-1452-46d3-933b-e60d6ccd4e9d.png)
(3)结合函数图象,请直接写出以下问题的答案.(结果保留一位小数)
①当
时,BC的长度约为_________.
②当
的三边中某一边的长度为
时,BC的长度约为__________.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d1f497a619e3b8dacbef4df817dc610.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32e00bf73d03dded1cf5f83cc5339361.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0923873d71674a89eba84e6fb5b2640d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32e00bf73d03dded1cf5f83cc5339361.png)
![](https://img.xkw.com/dksih/QBM/2021/5/17/2723067266187264/2781382295035904/STEM/5e730894-e028-4d85-b4fb-257696e4357f.png)
(1)根据点C在OB上的不同位置,画出相应的图形,测量线段OD,DE的长度,得到下表的几组对应值.
![]() | 0.0 | 1.0 | 2.0 | 3.0 | 4.0 | 5.0 | 6.0 | 7.0 | 8.0 | 9.0 | 10.0 |
![]() | a | 9.7 | 8.8 | 8.1 | 7.3 | 6.3 | 5.3 | 4.1 | 2.8 | 1.4 | 0 |
![]() | 14.1 | 12.7 | 11.2 | 9.8 | 8.2 | 6.7 | 5.2 | 3.7 | 2.4 | 1.1 | 0 |
②OE与自变量BC的长度具有某种关系,所以无需测量OE,通过推理并计算可以得到,请说明理由.
(2)在同一平面直角坐标系
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54015ff5b49e3283901da1291b6b921d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46f6872ffb1934339c53c2c2282d5889.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46f6872ffb1934339c53c2c2282d5889.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54015ff5b49e3283901da1291b6b921d.png)
![](https://img.xkw.com/dksih/QBM/2021/5/17/2723067266187264/2781382295035904/STEM/156fcfe7-1452-46d3-933b-e60d6ccd4e9d.png)
(3)结合函数图象,请直接写出以下问题的答案.(结果保留一位小数)
①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e393a210bd76b5a7499c64b822c3f07b.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32e00bf73d03dded1cf5f83cc5339361.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce710269ec0786472cad1bb73ee7d3ad.png)
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6 . 如图,抛物线
与
轴交于点
、
,与
轴交于点
,已知
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/21/c545a400-394f-4f29-9843-2d12de649258.png?resizew=150)
(1)求
的值和抛物线的顶点坐标;
(2)若直线
对应的函数表达式为
,则关于
的不等式
的解集为_________;
(3)连接
,
为抛物线上一点,若
,求点
的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/571d63b988ee57ed0833192a791d7463.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.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/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7291b3d921f595f28960abcdce6dfbed.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/21/c545a400-394f-4f29-9843-2d12de649258.png?resizew=150)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15b256345d7109e081b7c895591e995d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/328b4589bd538ba9ab22eaf270b5a3f2.png)
(3)连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b44ac8c782bf34396ff8c8d2fe6022b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
您最近一年使用:0次
7 . 如图,直线
:
与坐标轴交于A、D两点,以
为边在
右侧作正方形
,过C作
轴于G点.过点C的反比例函数
与直线
交于E、F两点.
(1)求证:
;
(2)求E、F两点坐标;
(3)填空:不等式
的取值范围是______.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1d7df623642896d720d6956ed1f0ff6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e548b39eb82898cf0389f575453853f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45bd7e92dae1e0c2af6c33d5e202f544.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/30/9eeafb46-1749-41d6-bcbe-146e0b034e17.png?resizew=216)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47593ae7e2c42e2e517001ddd64e0909.png)
(2)求E、F两点坐标;
(3)填空:不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ff14b6eb4e23bd9d0966cb797b89c56.png)
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8 . 如图,已知在
中,
,
,点D为边
上一动点(与点B、C不重合),点E为
上一点,
,过点E作
,垂足为点G,交射线
于点F.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/20/f29433a3-0d10-4751-aba6-9f340a2e174d.png?resizew=291)
(1)如果点D为边
的中点,求
的正切值;
(2)当点F在边
上时,设
,
,求y关于x的函数解析式及x的取值范围;
(3)连接
,如果
与
相似,求线段
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd967903ed5a6f640a5b801ec8be0070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed10df4140819d5451773a45de66201b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b37750daa8ba3b3fe3e9e2092f81c848.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e2b597f63fffe9531ed0cc3a3961c3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab1a1fd2fc33e89f357cef772ff6cd0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/20/f29433a3-0d10-4751-aba6-9f340a2e174d.png?resizew=291)
(1)如果点D为边
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4189a0821a0ffab9dc171ecd279ba442.png)
(2)当点F在边
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd4a7d7c2253a1686c61f8b8f3f6c6a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b290efb9f94c6d30cffb5973a78d9ec.png)
(3)连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5df7626240940eb340420a605e95aeee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddbf5459b20ca890a47ebf8d51d90cc2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
您最近一年使用:0次
2023-04-14更新
|
192次组卷
|
11卷引用:上海市杨浦区2020-2021学年九年级上学期质量调研数学试题(一模)
上海市杨浦区2020-2021学年九年级上学期质量调研数学试题(一模)上海市杨浦区2020-2021学年初三上学期数学一模2021年浙江省绍兴市越城区初中学业考试适应性测试数学试题上海市徐汇区2022-2023学年九年级上学期数学期末试卷(一模)(已下线)考点14 代数几何综合问题(二)(运动型探究问题)-2021年《三步冲刺中考·数学》(上海专用)之第1步小题夯基础(已下线)热点04 一次方程(组)与二元二次方程(组)-2021年中考数学【热点·重点·难点】专练(上海专用)(已下线)热点01 计算方程不等式问题-2021年《三步冲刺中考·数学》(上海专用)之第2步大题夺高分(已下线)上海卷05-2021年《三步冲刺中考·数学》(上海专用)之第3步中考热身卷(已下线)黄金卷01-【赢在中考·黄金8卷】备战2023年中考数学全真模拟卷(上海专用)(已下线)2023年上海市一模(几何综合)上海市长宁区华政附中2023-2024学年九年级上学期期中数学试题
9 . 在平面直角坐标系中,点
为坐标原点,直线
交
轴于点
,交
轴于点
,
,
.
![](https://img.xkw.com/dksih/QBM/2022/5/18/2982055378288640/2982830239268864/STEM/11d06cee-a75b-4830-ac1d-f6af2211d469.png?resizew=539)
(1)如图1,求
和
的值;
(2)如图2,点
在
轴负半轴上,过点
作
的垂线,垂足为点
,交线段
于点
,设点
的横坐标为
,线段
的长为
,求
与
之间的函数关系式,不要求写出自变量
的取值范围;
(3)如图3,在(2)的条件下,点
在
上,连接
,将线段
绕点
逆时针旋转得到线段PF(点F为点C旋转后的对应点),PF交CD于点G,点H在PC上,连接
,
,连接
和
,若
,
的面积为5,
,求
的正切值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c15fb18163df0690365a0d2e7ee88f5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5305bcbc56de59c64075adf9a87e5977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9620e97567191461f1a87aebb7b4f69.png)
![](https://img.xkw.com/dksih/QBM/2022/5/18/2982055378288640/2982830239268864/STEM/11d06cee-a75b-4830-ac1d-f6af2211d469.png?resizew=539)
(1)如图1,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)如图2,点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(3)如图3,在(2)的条件下,点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71b63d2504bd3ecce8c10560b142356f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4cd68cc82e90a5e2049a7ea3171b84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37b19514436278e1bd49c0ca9aa285ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c83f1f880e5ffbff036953acaca90c41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42887d9bf31c1dd99f13c39e63c9ab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6167238ad28ca721c6b172cd75f4ed5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e6ddd0810c99a69fc542f7d4d204536.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d55efe811de590f010338d0ad5bf67d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4861f542d231b95d9833728d5f0a4005.png)
您最近一年使用:0次
10 . 已知:如图,抛物线y=ax2﹣2ax﹣3a交x轴正半轴于点A,负半轴于点B,交y轴于点C,tan∠OBC=3.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/24/8eaec35c-8670-4de7-9b7f-0932c2b119c7.png?resizew=457)
(1)求a值;
(2)点P为第一象限抛物线上一点,连接AC、PA、PC,若点P的横坐标为t,△PAC的面积为S,求S与t的函数解析式,(请直接写出自变量t的取值范围);
(3)在(2)的条件下,过点P作PD∥y轴交CA延长线于点D,连接PB,交y轴于点E,点Q为第二象限抛物线上一点,连接QE并延长分别交x轴、抛物线于点N、F,连接FD,交x轴于点K,当E为QF的中点且FN=FK时,求直线DF的解析式.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/24/8eaec35c-8670-4de7-9b7f-0932c2b119c7.png?resizew=457)
(1)求a值;
(2)点P为第一象限抛物线上一点,连接AC、PA、PC,若点P的横坐标为t,△PAC的面积为S,求S与t的函数解析式,(请直接写出自变量t的取值范围);
(3)在(2)的条件下,过点P作PD∥y轴交CA延长线于点D,连接PB,交y轴于点E,点Q为第二象限抛物线上一点,连接QE并延长分别交x轴、抛物线于点N、F,连接FD,交x轴于点K,当E为QF的中点且FN=FK时,求直线DF的解析式.
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