1 . 抛物线
(
,
为常数,
)顶点为
,与
轴交于点
,
(点
在点
左侧),与
轴交于点
,直线
过点
且平行于
轴,
为第一象限内直线
上一动点,
为线段
上一动点.
(1)若
,
.
①求点
和点
,
的坐标;
②当点
为直线
与抛物线的交点时,求
的最小值;
(2)若
,
,且
的最小值等于
时,求
,
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc5ccf9df767bb1f45c668bf4bc6df87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cec12441802f71e803efaf2c62ee588.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03837b3769eda7f0d3804cc5ad4a6d60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcb5bac75f36bb1dc5c8190d4dbe681d.png)
①求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
②当点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eef7afc34443473b44d781a5d06bff02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a7847bff0073127f10ec3925127414.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/011f66c884442a8fc55829d46c71924d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41322821ce31416fdac8dd6e0aa41c71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
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2 . 图中是一个由
个相同的正方体组成的立体图形,它的主视图是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91e07104b699c4012be2d26160976a2.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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3 . 下列各式中,是关于
,
的二元一次方程的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2卷引用:广西壮族自治区桂林市国龙外国语学校2023-2024学年七年级下学期期中数学试题
4 . 如图,在正方形
中,
是对角线
,
的交点.过点
作
,分别交
,
于点
,
.若
,
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.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/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0acc3b50b12699a4a9a4cc391b8f5bcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.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/86338536656046e93b53672ade9a78b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3362a45b72536c714c5107b0ae94f1c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a71a9d21f77e9535de152bb33f802bb.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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5 . 数字
万用科学记数法表示应为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1480672ec92c4698aac745b029ad8d9.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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6 . 课本再现
如图
,
是
的直径,
.
(1)求
的度数.
拓展延伸
(2)如图
,若
,
与
的交点记作
,
.
①求
的半径;
②如图
,若
是
的切线,且点
在
的延长线上,求图
中阴影部分的周长.
如图
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c81131259f548e8803da8dec25fb644c.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2947ca8e0cdbeb4aab80ce9e7b63ba98.png)
拓展延伸
(2)如图
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2076ab9281325aedd252b9b5e70037b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30b0393ce62b24aa5f9b740d4cc6743b.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
②如图
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dea2ae9d515f9ab351ad72306b776ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
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名校
7 . 如图,在
中,
,若
,
,则
的长为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c0aa4c793921fdaa5d430cb90d78ca6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6295035b5fd1bdd674a54c1e8cdc73b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eca7e1a727ba332984ad857b3d25344d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
A.4 | B.6 | C.8 | D.10 |
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8 . 如图是由几个完全相同的小正方体组成的立体图形,它的主视图是( )
A.![]() | B.![]() | C.![]() | D.![]() |
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2卷引用:云南省2024年九年级下学期月考数学试题
名校
9 . 我国古代数学名著《九章算术》中对正负数的概念注有“今两算得失相反,要令正负以名之”.如:节约水
记作
,那么浪费水
应记作( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/635446403b6f971ccae7fb80297dd635.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22510a6c981bfd8c5ad4acef9c7a9f5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22a5fd582d80bbec9823269d993fd0d8.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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10 . 2023年5月17日10时49分,我国在西昌卫星发射中心成功发射第五十六颗北斗导航卫星,北斗系统作为国家重要基础设施,深刻改变着人们的生产生活方式.目前,某地图软件调用的北斗卫星日定位量超3000亿次,将数据3000亿用科学记数法表示为_____________ .
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