1 . 在平面直角坐标系
中,点
,连
,若线段
分别交曲线
于点
(异于点
),若
,则
的值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/772e230c06bb4a08780f2d78273f379a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a817cadf8bc4f29fb811c8e3e5a2184.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a817cadf8bc4f29fb811c8e3e5a2184.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92a37e8519ea115c1777d031d9963583.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91e1e4115d78e625e9e0f47cdade3286.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c8a4b91763add3ee3a9f0dc1937398d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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2 . 在平面直角坐标系
中,抛物线
经过点
和
,且在
轴上截得的线段长为
.
(1)求抛物线
的解析式;
(2)已知点
在抛物线
上,且在其对称轴右侧,点
在抛物线
的对称轴上,若
是以
为斜边的等腰直角三角形,求点
的坐标;
(3)将抛物线
向左平行移动3个单位得到抛物线
,直线
与
交于
两点,直线
与
交于
两点,若
分别为线段
和线段
的中点,连
,求证:直线
过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41c7a611e99d7785f66cd22fd8ee5e41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fec40ff4479edca2ed18b6cadb8db72f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01e8b766829220981993a9bd024e6b79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41322821ce31416fdac8dd6e0aa41c71.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(3)将抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa841ce5d58b64f747a3c1b69bb20a5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5f5921423b5d7a0723968a8e32d974a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c0f067a2a348ceb24a408f82992eab8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42887d9bf31c1dd99f13c39e63c9ab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
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3 . 在菱形
中,
,点
分别在边
上,将
沿着
对折,使点
恰好落在对角线
上的点
,若
,则
的面积等于__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a6f36741b86f464be362b12bac13d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea77ba313fcc751481ac1ca214df3fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c105d6ba18fbb0581fb982175e2eac9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5623355e6ec26ddfe095a7361a8f7aa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c105d6ba18fbb0581fb982175e2eac9.png)
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4 . 如图,等边
内有一动点
是等边三角形(点
在直线
两侧),直线
与直线
交于点
.
的大小是否为定值?若是定值,求出其大小;若不是定值,请说明理由.
(2)若
,求线段
长的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e428e7a09732be85c1224e9c8f6a71c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c856f329068123c34ad5c5c2c3dd5ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9521effc99744da7d1445af9681a3ef.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/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ed24d7acba0b3a7ebf4d520296424a3.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e72613c053b42aff06d307f2bf662ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
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5 . 如图,点
是正方形
的边
上一动点(异于
),连
,以
为对角线作正方形
与
交于点
,连
.
三点共线;
(2)若
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/526768fab505a5637e515731c9940380.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9c15e609c856cb7856d6101aa198fef.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5ab52edccf02d432e0aaa4542a147bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/956c4a03127f33e7fb7acc3476f717ce.png)
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6 . 对于任意不为0的实数
定义一种新运算“#”:①
;②
,则关于
的方程
的根为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccc9b449710062494286a01537ecdc00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3d785aaa5c1be4b5728cf56b4727d7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/820023f3de39dffe868be95757ce76d2.png)
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7 . 把两个半径为8和一个半径为9的圆形纸片放在桌面上,使它们两两相外切,若要用一个圆形纸片把这三个圆形纸片完全盖住,则这个大圆形纸片的最小半径等于__________ .
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8 . 已知19个连续整数的和为380,则紧接在这19个数后面的21个连续偶数的和是__________ .
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9 . 将4046减去它的
,再减去余下的
,再减去余下的
,再减去余下的
,依次类推,直至最后减去余下的
,则最后余下的数为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56d266a04f3dc7483eddbc26c5e487db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e1cc1f5992de67604d7b20513ef57d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d9172b506339c2bb7e67832b784a3af.png)
A.4 | B.3 | C.2 | D.1 |
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10 . 如图,等腰
两腰
分别交
于点D,E,点A在
外,点B,C在
上(不与D,E重合),连结
.已知
,设
.
,求
的度数;
(2)若
,求
的值;
(3)设
的周长分别为
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e428e7a09732be85c1224e9c8f6a71c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dec2ca6438c82b43f746057d8129885.png)
![](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/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b60b1106dab7a5191351381230d90ea8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ad6f5682533d502818a2ae3701f93ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0fb631298eea30835e48b6952fbe897.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d777d15cd733338ecfd0ea63819f62c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0c44512cb86bcf48c6d21357f45b533.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92d71107894329b293117036013dcbda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f1536777e064d5765378c1ffbf22be8.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d354fdeadccca97ddb6065187642502.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54fd86c0b61597f7adeef9b43f5a2504.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9da93a94458d257d7383a88922130011.png)
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