名校
1 . 如图所示,在平面直角坐标系中,矩形
的边
,边
,直线
:
与矩形
的边
和
都有交点,交点分别是点
与点
.
的代数式分别表示点
和点
的坐标:
______,
______;
(2)当四边形
为平行四边形时,求
的值;
(3)若要使在平面内存在点
,使以点
、
、
、
这四点为顶点的四边形为菱形,是否存在满足条件的
的值?若存在,求出
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3241d7fedd89d85711acd7a2635298af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f08273d339dc5ddbb89aa67bb8205e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e3dfcd8aff269dd5aba398816490c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bebb3b7f47e0decd48e64cb32aaa5903.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3241d7fedd89d85711acd7a2635298af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/828628c0876b45381c9a0edeb0fec236.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](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/2c94bb12cee76221e13f9ef955b0aab1.png)
![](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/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)当四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bc1cbcd6d00f0c36bad8254297d9f33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(3)若要使在平面内存在点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
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2 . 如图,四边形
是王大爷家的一块平行四边形田地,P为水井,现要把这块田地平均分给他的两个儿子,为了方便用水,要求两个儿子分到的地都与水井相邻,请你设计一下.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
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2024-05-06更新
|
78次组卷
|
2卷引用:江苏省宿迁市2023-2024学年八年级下学期第一次月考数学试题
3 . 抛物线
(b、c为常数)与x轴交于
、B两点(A点在B点左侧),与y轴交于点
.点P在该抛物线上且在x轴上方,设其横坐标为m.
(1)直接写出b,c的值:
_____,
______;
(2)连结
、
.当
时,求m的值;
(3)过点P作x轴的平行线与直线
交于点Q,
两点的距离记为d.请直接写出根据d的不同取值所对应的点P个数情况.(补充说明:当两点重合时,记
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58d88bbd34102b55fa928e8ff83f0d52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0929421a6188c3122442866b0b85a5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c052d7af2f98d95bac8725b608fba0fc.png)
(1)直接写出b,c的值:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ccd4162c7d09f970cb77cadacdbe521.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4e9bb42376c12d7d21702ae8062b25a.png)
(2)连结
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e66023e340d95e89e83c6896faf71fd4.png)
(3)过点P作x轴的平行线与直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85fa64abb0036dbff6a29f01b0c03899.png)
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4 . 如图,在平面直角坐标系中,正方形
的顶点O与坐标原点重合,点A的坐标
,点C在x轴正半轴上,点E从A出发以每秒1个单位长度向B运动,点F从C出发以每秒2个单位长度向O运动,当点F运动到点O时,点E也随之停止运动.设运动的时间为t秒.
为直径的圆与
相切时,求t的值;
(2)求证:在E、F的运动过程中,直线
过定点,记为点Q,并求出定点Q的坐标;
(3)在(2)的条件下,将
沿
翻折,得
,(点C的对应点是点
),当
是直角三角形时,求t的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3241d7fedd89d85711acd7a2635298af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f88a1f304d24f867811ff75447f50f15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
(2)求证:在E、F的运动过程中,直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
(3)在(2)的条件下,将
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2d16438549a3008189e8112c624eee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b8db072e2b6104671b82f948012fb45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1b1d0b5a8cd3eb137cd6de0903d814.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c8a9c4957431681ddfc77895a88508.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39ca6e3b489a57fd006f769e997558f5.png)
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名校
5 . 某校准备举行心理健康知识竞赛,先以班级为单位进行预赛,每班再选取前2名进入决赛,某班共有50名学生,根据预赛成绩绘制成下列图表,请根据图表提供的信息,解答下列问题.
预赛成绩频数分布表
______,
_______;
(2)请把预赛成绩频数分布直方图补充完整;
(3)若学校有500名学生,在预赛中考满90分的大概有多少名学生?
(4)在这次预赛中,某班有3位同学甲、乙、丙获得满分,现通过随机抽选的方式决定参加决赛的人选,请问甲、乙同时参加决赛的概率是多少?(请用“画树状图”或“列表”等方法写出分析过程)
预赛成绩频数分布表
预赛成绩
| |||||
频数 | 4 | 6 | 20 | 5 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ccd4162c7d09f970cb77cadacdbe521.png)
(2)请把预赛成绩频数分布直方图补充完整;
(3)若学校有500名学生,在预赛中考满90分的大概有多少名学生?
(4)在这次预赛中,某班有3位同学甲、乙、丙获得满分,现通过随机抽选的方式决定参加决赛的人选,请问甲、乙同时参加决赛的概率是多少?(请用“画树状图”或“列表”等方法写出分析过程)
您最近一年使用:0次
2024-04-25更新
|
87次组卷
|
2卷引用:江苏省无锡市侨谊中学年2023-2024学年九年级下学期数学3月月考试题
6 . 下列事件中,属于随机事件的是( )
A.平行四边形的对角相等 | B.![]() |
C.明天太阳从西方升起 | D.小明买彩票将获得500万元大奖 |
您最近一年使用:0次
2024-04-24更新
|
57次组卷
|
2卷引用:江苏省无锡市宜兴市桃溪中学2023-2024学年八年级下学期月考数学试题
7 . 如图,
中,
,
,点
为平行四边形边
上一动点,连接
,将
绕点
逆时针旋转
得线段
,点
的对应点是
.
①当
,点
落在直线
或直线
上时,直接写出此时
的长为 ;
②连接
,求证:
的面积是一个定值.
(2)如图2,当
时,连接
,将
绕点
逆时针旋转
得线段
,点
的对应点是
.直接写出
是等腰三角形时
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5138a9f70d5e8b0580e30fef6eb7baef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76d527d4795ece4a5756d1cf8dba31e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57612cb0e5a7e43d51cc33738bb7550d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88929f4ba0851730d5f941d426b87548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13af018556f0b484ed38519f2edc791c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30513ea48bc1ef3ae78adac83d894f14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7a0387fc1258f31e44a10068c0ccfd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/143e346ac3950f60077291dda2be73c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3953cec61ac602ce5eb59b7912352179.png)
①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2ab8b9338fbcdf04d0e703337ea34f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3953cec61ac602ce5eb59b7912352179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88929f4ba0851730d5f941d426b87548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764509115979e9958101808383672ec0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80672dda9430cb42b3136bcb1b67bbad.png)
②连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbf9d83e22c28a9ac56d5a8b6d02b104.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19343455668abab3ca3b05aa2cf616c2.png)
(2)如图2,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02b6e6b9a38932e653e053f1895b1bae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4d260c4df7b0dc180af6980d21f3371.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4d260c4df7b0dc180af6980d21f3371.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7a0387fc1258f31e44a10068c0ccfd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7096fdcee49451970e84214dee5c2e5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c8a9c4957431681ddfc77895a88508.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b37ea9f8c4f8d1853769337277b6af3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d48943db264c08adaf6ae0766fd56459.png)
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解题方法
8 . 在平面直角坐标系
中,抛物线
与
轴交于
,
两点,若
,函数
的最小值为
,且
.
(1)求该抛物线的解析式;
(2)如果将该抛物线在
轴下方的部分沿
轴向上翻折,得到的图象与剩余的图象组成新图形
.当函数
的图象与图形
的公共点的个数大于
时,求
的取值范围;
(3)在(2)的条件下,当
取最大值时,函数
的图象与图形
的对称轴交于点
,若过
作平行于
轴的直线交图形
于点
,过点
作
轴的平行线交函数
的图象于点
,
为线段
上的一点,动点
从点
出发,沿
运动到点
停止,已知点
在
上运动的速度为
单位长度每秒,在
上运动的速度为
单位长度每秒.求当点
运动的时间最短时,对应的点
的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f2beb91f10d2d8f2aa0dcc3f5cd1598.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/526bb5b206810f46a51d960f58510779.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/fa375c3888b332f24e7d0f9b9600c694.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/526bb5b206810f46a51d960f58510779.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/087c617ff25126d2cd6428b2cd62ff47.png)
(1)求该抛物线的解析式;
(2)如果将该抛物线在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c66f7e66125423be8450b85ab40bf15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(3)在(2)的条件下,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c66f7e66125423be8450b85ab40bf15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](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/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e09b5ab0311ddf7b757b3273e0d4e77c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be8d447a867fca2de04222a72885b659.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ec2dd56f2e4c3ae762cfb807ec7d90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d1b3406c05ed581cbb0532f26052c0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2967337e3fcb228dded64ab0c41a17e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d48943db264c08adaf6ae0766fd56459.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
您最近一年使用:0次
名校
9 . 尺规作图(保留作图痕迹).
(1)已知:如图,A、B是
上任意两点,求作:
的直径
,使
;
内任意两点,求作:
的直径
,使
.
(1)已知:如图,A、B是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7de966c316db1013defc56372fcf814e.png)
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2卷引用:江苏省无锡市江南中学2023-2024学年九年级下学期3月月考数学试题
10 . 若点
在第四象限,点
的坐标为
,则
的面积为8,则
的值______
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e717fc336c2b9c1617421b5b8a4ae6b3.png)
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2卷引用:江苏省南通市通州区通州区育才中学2023-2024学年七年级下学期3月月考数学试题