1 . 当
且
时,
对一切
,
恒成立.学生小刚在研究对数运算时,发现有这么一个等式
,带着好奇,他进一步对
进行深入研究.
(1)若正数
,
满足
,当
时,求
的值;
(2)除整数对
,请再举出一个整数对
满足
;
(3)证明:当
时,只有一对正整数对
使得等式
成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f62d7d74585d13636e5c167a775cb227.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b140e221ddf537b8964fff8557cca0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de8610232c77741a37463feba1a66c94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8f81a1bedc557556e614309feead266.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3703709b06e37fb0ed1e7b47f346eef1.png)
(1)若正数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3703709b06e37fb0ed1e7b47f346eef1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94174f37421d296a192b2df66c05f875.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(2)除整数对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29343388ca8b33dc98325e65382b38a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba7204f43679af6935e494c59d40c6ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3703709b06e37fb0ed1e7b47f346eef1.png)
(3)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e34f42b3be15518c29e3689c9fe6d6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba7204f43679af6935e494c59d40c6ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3703709b06e37fb0ed1e7b47f346eef1.png)
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2024-06-08更新
|
211次组卷
|
2卷引用:温州人文高级中学2023-2024学年高一年级下学期5月月考数学试题
名校
2 . 小明同学在计算出8个数的平均数后,不小心将这个数也混到数据中了,那么重新计算这些新数据后一定不变的量是( )
A.平均数 | B.中位数 | C.众数 | D.方差 |
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3 . 定义:若四边形有一组对角互补,一组邻边相等,且相等邻边的夹角为直角,像这样的图形称为“直角等邻对补”四边形,简称“直等补”四边形.
(1)如图1,正方形ABCD中,E是CD上的点,将
绕B点旋转,使BC与BA重合,此时点E的对应点F在DA的延长线上,则四边形
为“直等补”四边形,为什么?
(2)如图2,已知四边形
是“直等补”四边形,
,
,
,点
到直线
的距离为BE.
①求
的长;
②若
分别是
边上的动点,求
周长的最小值.
(1)如图1,正方形ABCD中,E是CD上的点,将
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbfa1a2af7e38d33634c462300df381f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2330c01a4d2b5b20f106e3e48834d5c0.png)
(2)如图2,已知四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59fe75f967e8915c9124a5d4ac420a4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/037b342a682cbd4241855a243da3c016.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/deb6694f3443cc5f4d09948679251b61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9df7fc746f8c4801d8f2f0471ba3297e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e856c15c61d7cb6ebd8daef542a4e7f.png)
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4 . 已知在平面直角坐标系中,直线
交坐标轴于A、B两点,直线
交坐标轴于C、D两点,已知点
,
.
与
交于点E,试判断
的形状,并说明理由;
(2)点P、Q在
的边上,且满足
与
全等(点Q异于点C),直接写出点Q的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85e24de76e6f9a6097f890bc2f395904.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a01e2e3d40112fdeeb464f81eaac1c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5eae074b97ec3ff58fbd9d556aea81f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a5a48393681b882d719f5562235ba11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcb49df05f2e31d005735c3f14a21d30.png)
(2)点P、Q在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcb49df05f2e31d005735c3f14a21d30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9dc427a01582ec222446b352d40ab0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea1f0417d8269f01d8e0bc1a8756e2ac.png)
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5 . 如图,在平面直角坐标系中,抛物线
经过
、
、
.
(2)点D是线段BC上一动点,点D关于AC、AB的对称点分别为点M、N,连接MN交线段AC、AB于E、F.求
最小值;
(3)在(2)的条件下请直接写出线段MN的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a90385c676848de67293e3ed6bc000fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da6bbbb53aaeab0ab7a242228cc510fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fec0bc3a43265b63b6964476ca327fab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/850e01debd266a398b597a1876dbb3ea.png)
(2)点D是线段BC上一动点,点D关于AC、AB的对称点分别为点M、N,连接MN交线段AC、AB于E、F.求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13106b48acf096f7fc9ac1e49559b130.png)
(3)在(2)的条件下请直接写出线段MN的取值范围.
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6 . 今年6月份,永州市某中学开展“六城同创”知识竞赛活动,赛后,随机抽取了部分参赛学生的成绩,按得分划为A,B,C,D四个等级,
,
,
,
,并绘制了如图两幅不完整的统计图,请结合图中所给信息,解答下列问题:
(2)扇形统计图中
______,
______,B等级所占扇形的圆心角度数为______.
(3)该校准备从上述获得A等级的四名学生中选取两人参加永州市举行的“六城同创”知识竞赛,已知这四人中有两名男生(用
,
表示),两名女生(用
,
表示),请利用树状图法或列表法,求恰好抽到1名男生和1名女生的概率.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b788f849213c9bede89249019d87808d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59e507529b30a6ff85a1f089bd31a7b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cbfd347f5c3a2ae250f732fa9ab849f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4965f1128f8c5a418c24e39a51c364c0.png)
(2)扇形统计图中
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c57bbef89a37f1a3808c0ceeac0c22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f3cb8d72bb2e281b943b3b430138ef7.png)
(3)该校准备从上述获得A等级的四名学生中选取两人参加永州市举行的“六城同创”知识竞赛,已知这四人中有两名男生(用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/024e2379c58191758f8bd7602a6bcb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b34a75c2a392f235c5f07b91d9fb58d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4450b959d69fdf09b38ba82fe132ec33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c89fcb4633216e492ed5a04cf45eed.png)
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7 . 将正三角形、正方形、正五边形按如图所示的方式摆放,其中正方形和正五边形的下底边是水平共线的,如果
,那么
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcc3ef6a72ecee9efdca1f447fa243d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cc310194575262fb45352c2fbc19868.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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8 . 如图,在矩形ABCD中,
,
,对角线AC、BD相交于点O,动点P、Q分别从点C、A同时出发,运动速度均为1cm/s,点P沿
运动.到点B停止,点Q沿
运动,到点C停止. 连接
,设
的面积为
(这里规定:线段是面积为0的几何图形),点Q的运动时间为x(s).
时,求x的值;
(2)当
时,求y与x之间的函数关系式;
(3)直接写出在整个运动过程中,使
的所有
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ee5bd6f04872ef8d3d833d0e2056161.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e40cc1f35e71e2abf5943a21fe448df4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82baca47182531f9f2135ef3056cc1ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3087da5c11909dab613378fee8d471fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31ed47b8230bc383b2c167264f750d70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9763846b1131e1e3e2d741ad95d5bb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/012b14b48c09eb820c49c13dccb642bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b10bb426e00de29d8664ca5babb2f4f3.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fc1a1c6781dc4554c47e2affb00405c.png)
(3)直接写出在整个运动过程中,使
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34ecd96adaec63c5bbd65f59f885ecfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
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9 . 有五本形状为长方体的书放置在方形书架中,如图所示,其中四本竖放,第五本斜放,点G正好在书架边框上,每本书的厚度为
,高度为
,书架宽为
,则FI的长______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3a9eed64d225267a58cd001db67e2a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbe9f7abf7bcf4e1aa2579cd191d7761.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e57171806f407a98dd8a796d4d2d6bbd.png)
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10 . 如图四边形ABCD与BEFG是并列放在一起的两个正方形,O是BF与EG的交点.如果正方形ABCD的面积是9,
,则
的面积为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb6f6c04bc017ced739230d14ba31948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/882475eea0be0fa89024b38d556fed0d.png)
A.1 | B.![]() | C.4 | D.![]() |
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