名校
1 . 图一所示,在平面直角坐标系中,抛物线
与x轴交于
,
两点,与y轴交于点C.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/22/60680793-2af4-4c55-a4e2-b4f9dc9eba59.png?resizew=120)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/22/f93df309-e8e7-4e20-b34d-80be466866ee.png?resizew=119)
(1)求抛物线的函数表达式及顶点坐标;
(2)点P为第三象限内抛物线上一动点,作直线AC,连接PA,PC,求
面积的最大值及此时点P的坐标;
(3)设直线
:
交抛物线于点M,N,求证:无论k为何值,平行于x轴的直线
:
上总存在一点E,使得
为直角.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/818ccf8040f189fff5665ec93892b2ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a525534689bd2701205d4ab17574c39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c850811ba59a05e945a665196539a048.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/22/60680793-2af4-4c55-a4e2-b4f9dc9eba59.png?resizew=120)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/22/f93df309-e8e7-4e20-b34d-80be466866ee.png?resizew=119)
(1)求抛物线的函数表达式及顶点坐标;
(2)点P为第三象限内抛物线上一动点,作直线AC,连接PA,PC,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fbfcae2cecc98e2d6c16dde6d3ec1c1.png)
(3)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff7cd2f34acbf4884ac6ea40b5d5be19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/216be086e1952cf1e782a7a3c132496e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/435f30095577dc714634354f5ad27715.png)
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2 . 如图,点E是
的内心,AE的延长线和
的外接圆相交于点D,与BC相交于点G,则下列结论:①
;②若
,则
;③若点G为BC的中点,则
;④
.其中一定正确的个数是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/22/e6fa31a7-d828-4c0b-943d-58d185b820ca.png?resizew=160)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ba77f66ecad8eb4a7a63f169f28a3b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b57fdd2a3642716fcf5100011eb3ec88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84ee8de2d272e8a3cad423ef206cd7eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f2549a1964e7221d4b82698d0afa9ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e792b0ef3d542237ed0903194597651.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/22/e6fa31a7-d828-4c0b-943d-58d185b820ca.png?resizew=160)
A.1 | B.2 | C.3 | D.4 |
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3 . 分数
、
和
的大小关系为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de1e0e5c853fc8a6ac14dc67f4d32f18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eae2ef7c8d46122e8b118a331d4d5136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/765b75d54a962031eadac01ae7a46e70.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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4 . 在初中数学文化节游园活动中,被称为“数学小王子”的王小明参加了“智取九宫格”游戏比赛,活动规则是:在九宫格中,除了已经填写的三个数之外的每一个方格中,填入一个数,使每一横行、每一竖列以及两条对角线上的3个数之和分别相等,且均为m.王小明抽取到的题目如图所示,他运用初中所学的数学知识,很快就完成了这个游戏,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c57bbef89a37f1a3808c0ceeac0c22.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c57bbef89a37f1a3808c0ceeac0c22.png)
16 | ||
7 | ||
4 |
您最近一年使用:0次
2023-11-23更新
|
83次组卷
|
2卷引用:湖南师范大学附属中学2023-2024学年高一上学期入学考试数学试题
5 . 在平面直角坐标系中,抛物线
与
轴相交于点
,
点
在点
的左侧
,与
轴相交于点
,连接
.
(1)求点
,点
的坐标;
(2)如图
,点
在线段
上
点
不与点
重合
,点
在
轴负半轴上,
,连接
,
,
,设
的面积为
,
的面积为
,
,当
取最大值时,求
的值;
(3)如图
,抛物线的顶点为
,连接
,
,点
在第一象限的抛物线上,
与
相交于点
,是否存在点
,使
,若存在,请求出点
的坐标;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17d794141572c8b1e70957754f32b9eb.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/3a920a78c48e71749017d40e01caa3a3.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/04582116cd765fcc5a52f44279ad6c94.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://img.xkw.com/dksih/QBM/editorImg/2023/10/18/7c2cc2a6-5942-42ba-81da-8cc803409dd1.png?resizew=125)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/18/1da7920e-41a6-4f49-b614-68ebde2448f2.png?resizew=125)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)如图
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5850ed6ad7d8e9652625bd03766c61df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd995178601c2ad7b40f973d268c7bb7.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/04582116cd765fcc5a52f44279ad6c94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcf2e3236ea30ee2c37928b98041f13a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54fb6e81fee5674c3e26a65e58cc506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f2ea13010e2399194be2a681310543e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52e6151dc6ef89bc79b1ca0dc63b291e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)如图
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f91ebc37c87bdb305a7d8276888a6b93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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6 . 阅读材料,完成相应任务:“贾宪三角”又称“杨辉三角”,在欧洲则称为“帕斯卡三角”
如图所示
,它揭示了
为非负数
展开式的各项系数的规律.
(1)直接写出
_____.
(2)
的展开式中
项的系数是_____.
(3)利用上述规律求
的值,写出过程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd995178601c2ad7b40f973d268c7bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e130e4eb6e7e001fe6f17ca1c11e421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
(1)直接写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c48e3296ee038094de94e9a7b84416dd.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/233137c88924a328fba3fd740f376929.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)利用上述规律求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a2179f1de048d56cdab99abce419592.png)
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7 . 某学校为了丰富学生课余生活,开展了“第二课堂”的活动,推出了以下四种选修课程:
绘画;
唱歌;
演讲;
十字锈
学校规定:每个学生都必须报名且只能选择其中的一个课程
学校随机抽查了部分学生,对他们选择的课程情况进行了统计,并绘制了如下两幅不完整的统计图
请结合统计图中的信息,解决下列问题:
(1)这次学校抽查的学生人数是_____;
(2)将条形统计图补充完整;
(3)求扇形统计图中,
课程部分的圆心角的度数;
(4)如果该校共有
名学生,请你估计该校报
的学生约有多少人?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f3edd98816dcf1b2ea50d630a565420.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/979426d711e6b4ddcefc44f92d8a9062.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8d30bb07aa3a594041266cdfdeb42ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09e7170bb4a2ddcef39391a06c989162.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c90282d4a37c9a20620d4bbb0c263cae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c90282d4a37c9a20620d4bbb0c263cae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c90282d4a37c9a20620d4bbb0c263cae.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/18/2298a300-b120-4c2b-adf9-32e47adddc9b.png?resizew=394)
(1)这次学校抽查的学生人数是_____;
(2)将条形统计图补充完整;
(3)求扇形统计图中,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(4)如果该校共有
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dadc63e6e33743ce590ed968948a5a58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
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8 . 计算:
(1)
;
(2)解方程:
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ea47d7a1a9e3b5a2d52cd1b725c0f77.png)
(2)解方程:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/544b2bbd3d92cbc295f8884cafc296d6.png)
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名校
9 . 火车匀速通过长
米的铁桥用了
秒,如果它的速度加快
倍,通过
米长的铁桥就只用了
秒,求这列火车的长度为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cbcf82603580ddba4cfdb4efde85a8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f76fba0fe83cf0aa9a68210591cac1a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1872505e520fc86ff7e49d2e54903fa0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c748e40ba21ac5063d3bccaa57ef278.png)
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2023-10-02更新
|
28次组卷
|
2卷引用:湖南省岳阳市第十三中学2023-2024学年高一上学期入学考试数学试题
名校
10 . 如图,用若干根相同的小木棒拼成图形,拼第
个图形需要
根小木棒,拼第
个图形需要
根小木棒,拼第
个图形需要
根小木棒
若按照这样的方法拼成的第
个图形需要
根小木棒,则
的值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8c4c029e552954bd493b49aeab82d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c7f959148f8da15d2a4a4ceb30745df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f573bd1591735843cc5852535af976f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07096af3b99fd1cb11c31f19a2c6408e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb80913fc086c6a264ed476d193e7344.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/18/47547680-fc45-4adc-b7d1-f410ad68c809.png?resizew=372)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2023-10-02更新
|
46次组卷
|
2卷引用:湖南省岳阳市第十三中学2023-2024学年高一上学期入学考试数学试题