1 . 如图,在平面直角坐标系中,直线
与x轴交于点B,与y轴交于点A,以x轴为对称轴作直线
的轴对称图形直线
,点
,
,
,…在直线
上,点
,
,
,…在x轴正半轴上,点
,
,
,…在直线
上,若
,
,
,…,
均为等边三角形,菱形
,菱形
,菱形
……菱形
的面积分别是
,
,
,…,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04c2864e2ec3416cc4c081ac1f71a0af.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77fc4501e9b3bf4c4fe2353d35c8c7cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75d2e50a6d7913fd23c79d2269b64bbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04b56e44e4f0424a2b7a45567120a2e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a71fc9c0068109dad1382354570665.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2857fac4963b129d99e79dcb3e13d295.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/809405c2105f8e91b87e21022cb48062.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6899bf9cadae2ccdb14cbc87d4f280ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04c2864e2ec3416cc4c081ac1f71a0af.png)
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2 . 一个扇形的弧长为
,这条弧所对的圆心角为
,则这个扇形的面积为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b51733ec6a4a8f02e00854fc75b8987.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a8f3a8b0608ec011ad95c522fd2ea4d.png)
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3 . 在一条笔直的公路上依次有
三地.甲、乙两车同时出发.甲车从
地匀速行驶到
地,休息1小时后掉头(掉头时间忽略不计),按原路原速返回到
地.乙车从
地匀速行驶到
地,到达
地停止行驶.在两车行驶的过程中,甲、乙两车距各自出发地的路程
(单位:千米)与甲车行驶时间
(单位:小时)之间的函数图象如图所示,请结合图象解决下列问题:
(2)求乙车从
地到
地的过程中
与
的函数解析式,并直接写出自变量
的取值范围;
(3)在乙车到达
地之前,甲车出发多少小时,甲、乙两车相距150千米?请直接写出答案.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.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/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)求乙车从
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(3)在乙车到达
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
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3卷引用:2024年黑龙江省伊春市九年级中考三模数学试题
4 . 在
中,
,
,点
分别在边
所在直线上,
,垂足为
,
.请解答下列问题:
在线段
上时,如图①,求证:
;
(2)当点
在线段
的延长线上时,如图②;当点
在线段
的延长线上时,如图③,请直接写出线段
之间的数量关系,不需要证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd967903ed5a6f640a5b801ec8be0070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c06154cae3bf7a8ce5a1e97a7380875.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dc9795efa99b6fb9fdf9778085dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/927456b0989846a2f1573844bbaa2105.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942e6dafcfcbf0682856b9f25178694d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/876bb8ce0ca53475fa091ffd18bdc94a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0a3600b1760a63a10c9a0429b439dc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d339586367796e4de39c802bcf0cc47f.png)
(2)当点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b1bd1adfe4cc6566218f19970c2fd3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4069744491e6aec3f4e8e237afdedb4.png)
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3卷引用:2024年黑龙江省伊春市九年级中考三模数学试题
5 . 如图,抛物线
与
轴交于点
,与
轴交于点
,连接
,
,若
,
.请解答下列问题:
(2)点
在第四象限的抛物线上,若
,则点
的坐标为 .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc229acc8bf1a2047394bda863b1ea71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.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/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/519d3cbe962154438e43a23b0d9eda2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92062ef1dbe461756d72a0b2bcc97424.png)
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b6980cd874bbdc406bef074e776aa33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
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3卷引用:2024年黑龙江省伊春市九年级中考三模数学试题
6 . 先化简,再求值:
,其中
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b6ded8ea0f0b84d343f53fdaaa06b1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6612877d9a039f8fa5267d590f7247c.png)
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3卷引用:2024年黑龙江省伊春市九年级中考三模数学试题
7 . 一只不透明的袋子中放有红、绿、白三种颜色的球各两个,它们除颜色外其他都一样,小明从袋子中摸出一个球后放回摇匀,再摸出一个球,则小明两次都能摸到白球的概率是________ .
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3卷引用:2024年黑龙江省伊春市九年级中考三模数学试题
8 . 不等式组
的解集为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892560dcff6af9f66a3f735652f69dd7.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23908cfb3bf616d99879bf2be8eeec39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24b843858ba23012c724dea0c51d54a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892560dcff6af9f66a3f735652f69dd7.png)
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3卷引用:2024年黑龙江省伊春市九年级中考三模数学试题
9 . 在函数
中,自变量x的取值范围是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/270c3b0dc0b47a13f7fd1a0b4bdb3662.png)
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3卷引用:2024年黑龙江省伊春市九年级中考三模数学试题
10 . 如图,E是矩形
的边
的中点,
于点F,
的延长线交
于点G,连接
,则下列结论:①
;②
;③若
,
,则
;④
;⑤图中相似三角形只有6对.其中正确结论的序号是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cb3f9a5da641be35117fd35ba07a6aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1ffb98f1e3c1317c0db403d3af04bdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/187ed13a7bd532bd39af5e5ad7493a2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79ff575e55857af133edb24c8e61504f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764509115979e9958101808383672ec0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a679040c4d556723e482bacbab41356d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f6b78e3a62d67bb720aebf1e2246ca8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44088e42f218a822101b56fea263ae1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faffe3765c15f53305516895aa595a9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21fe7f306533f388843ff62fa2b5251a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e906c2799998ba08e3b6da8d28c24d65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2555968c3266a4be0100327d858417fa.png)
A.①②③ | B.②③④ | C.①④⑤ | D.①②③④⑤ |
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3卷引用:2024年黑龙江省伊春市九年级中考三模数学试题