1 . 如图,点D在半圆O上,半径
,
,点C在弧
上移动,连接
,H是
上一点,
,连接
,点C在移动的过程中,
的最小值是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db6298ce944d2be70bc3fb1662f73397.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f26ad70d2b3aac8604834d57dfc59bb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57570f783a548fd32e1ae8e84bf9cb79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcdae78f4d3b8d8213ac3ac9a9567eb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcdae78f4d3b8d8213ac3ac9a9567eb5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/31/3dd32096-e099-4388-a708-c3ecd48680e7.png?resizew=164)
A.5 | B.6 | C.7 | D.8 |
您最近一年使用:0次
2 . 与实数
最接近的整数是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a87f408f95bc42376c765b2870d5803.png)
A.2 | B.3 | C.4 | D.5 |
您最近一年使用:0次
3 . 设二次函数
(
、
为常数,
),且
.
(1)若该二次函数的图象经过点
,求该二次函数的解析式;
(2)无论
取何常数,这个二次函数的图象始终经过一个定点,求出这个定点坐标;
(3)已知点
和
都在二次函数的图象上,若
,且
,求
的取值范围(用含
的代数式表示).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d27177205849d6f48ce61f323c76f9d9.png)
![](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/20849c00c47cbdc43f18d53341b6c4e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/086defd602b3cc9012ace0e077be0ce5.png)
(1)若该二次函数的图象经过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5548c101f84334ab651fd7139e324f4.png)
(2)无论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea9a7657ae37143d7a673720cf4731e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/532bd0bad965c65da450e7aac839e1e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f90560052fe43871fd3d594c771723c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7091d529281abff275ef19b9197445a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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4 . 在如图所示平面直角坐标系中,点
的坐标为
,点
的坐标为
,过点
作直线
轴,点
是直线
上的一个动点,将线段
以
为旋转中心逆时针旋转
得到
,连接
,
.
(1)如果点
的坐标为
,则
的值为____________;
(2)当
时,求出点
运动轨迹图象的表达式,并注明自变量的取值范围;
(3)求出
周长的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fab8a0cc6504aa4c3a38006f5394b4c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afa482d7bcaa385bfc3548b42a4bfb60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ccb7a14074460f0fd65dc22b5a767f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/732c018e69d42df32aaac87095890b81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c02b54dc6b3e1bb6544f47d4c8743fcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/1/b846f265-ac0f-48d4-8386-5485f42a2221.png?resizew=203)
(1)如果点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a70feb95addc50c555e2eb6ad82521ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17bda892497cea43df67db57b4e2a07a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(3)求出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e742966e3711cfa53dce04022acf4bcc.png)
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5 . 如图1,四边形
是某市休闲广场一个供市民休息和观赏的看台侧面示意图.已知:在四边形
中,
,
米,
,
.从底边
上点
测得点
的仰角
,且
米.
(1)求
的长度;
(2)如图2,为了避免白天市民在看台
和
的位置受到与水平面成
角的光线照射,想修建一个遮阳篷,求这个遮阳篷的宽度
是多少米?(计算结果都保留根号)
![](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/10df84d553a8826a7ce9bff4bf0d95b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/479bb5e937f4fdb1fcbca229e62e0e80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6662097cf94dc37facdaba44b49966d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d875f0d9448d025bb6dfad47dd55fad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea147ada4f0aefdd3808a6a1133792eb.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/15/6c953625-fa9c-4167-ae8f-3aa2d846943e.png?resizew=396)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
(2)如图2,为了避免白天市民在看台
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b39addc1173a458af87ed5c5e3f06466.png)
您最近一年使用:0次
6 . 如图,四边形
是平行四边形,E为
上任意一点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/4/304dd5a3-182e-480a-a5e2-7e448d05a2b3.jpg?resizew=323)
(1)如图①,只用无刻度的直尺在
边上作出点F,使
;
(2)如图②,用直尺和圆规作出菱形
,使得点F、G、H分别在边
、
、
上.(不写作法,只保留作图痕迹)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/4/304dd5a3-182e-480a-a5e2-7e448d05a2b3.jpg?resizew=323)
(1)如图①,只用无刻度的直尺在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f40b3bf6b27f936e0747de92151a1f77.png)
(2)如图②,用直尺和圆规作出菱形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/611f100dcfa7803db6eb233e2e7f2dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67d822262ff00915910e5b87d81ad1ba.png)
您最近一年使用:0次
7 . 观察一组数据:1,1,2,3,5,8,13,…,它们有一定的规律,若记第一个数为
,第二个数记为
,…,第
个数记为
.
(1)计算
的值;
(2)请直接写出
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(1)计算
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a94b8898cb09f4063fe3ac0a4b5aa0d.png)
(2)请直接写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05006583e059c773d6e4d62de5401ceb.png)
您最近一年使用:0次
8 . 如图,已知直线
和
与
轴相交所成的锐角分别为
,点A坐标为
,点
为直线
上的一个动点,
为直线
上的两个动点,则
长度的最小值为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/20/6eb0c26d-0845-4a9e-aa1f-b0345ccb9652.png?resizew=152)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ccc754e3d0f4004bf4404665499688e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/022609adad9d3e0eae5b014cfd283b54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8e26f3e51c374fdeada0b0331701741.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f612078b0cdcf31f3c1afa8b0051c8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5db7fa56f5b94e6da72b6a126bde0844.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/20/6eb0c26d-0845-4a9e-aa1f-b0345ccb9652.png?resizew=152)
A.2 | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
名校
9 . 如图,
中,
于
,点
是
上一点,连接
并延长交
于点
于点
,连接
.
(1)如图(1),若
,求线段
的长度;
(2)如图(2),若
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19f848e46fa0dba74616877228fd8b81.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/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1002de3b40b782f143ccc477cf076aa6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e55e398e8520d8a36fb5a625a085b8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/21/9ef5fffa-2694-4e91-af44-55c444352825.png?resizew=419)
(1)如图(1),若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa476f087586ea5f440caed6ad1b9a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
(2)如图(2),若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e7e3dad1c0af37e5102a7af3424ea96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/929fe96d6330aca46c962c860ea99fe0.png)
您最近一年使用:0次
名校
10 . 某校举行春季运动会时,由若干名同学组成一个8列的长方形队列.如果原队列中增加120人,就能重新组成一个正方形队列;如果原队列中减少120人,也能重新组成一个正方形队列.原长方形队列有多少名学生?
您最近一年使用:0次