一、选择题(本大题共12小题,在每小题给出的四个选项中,只有一个是正确的,请把正确选出来,每小题选对得4分,选错、不选或选出的答案超过一个,均记零分)
-
1.
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmfrac%3E%3Cmrow%3E%3Cmn%3E5%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E6%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmfrac%3E%3C%2Fmath%3E)
的相反数是( )
-
-
3.
下面图形中,中心对称图形的个数有 ( )
![](//tikupic.21cnjy.com/2024/07/04/b6/12/b61241a41af7adee67a0d5497603b4f4.png)
A . 1个
B . 2个
C . 3个
D . 4个
-
4.
据泰山景区2024年1月4日消息,2023年泰山景区累计接待进山游客超860万人次,同比增长
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmn%3E3%3C%2Fmn%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmn%3E.%3C%2Fmn%3E%3Cmn%3E3%3C%2Fmn%3E%3Cmn%3E6%3C%2Fmn%3E%3Cmn%3E%25%3C%2Fmn%3E%3C%2Fmath%3E)
, 剧新了历年游客是最高纪是.数据860万用科学记数法表示为 ( )
-
5.
如图,直线l∥m,等边三角形ABC的两个顶点B,C分别落在直线l,m上,若∠ABE=21°,则∠ACD的度数是( )
![](//tikupic.21cnjy.com/2024/07/15/f4/ed/f4eded4f853425767c85bc5c5a032a74.png)
-
6.
如图,AB是⊙O的直径,C,D是⊙O上两点,BA平分∠CBD,若∠AOD=50°,则∠A的度数为( )
![](//tikupic.21cnjy.com/2024/07/15/76/30/7630f8413458f512a8c0bcc3e59bb8e6.png)
-
7.
关于
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Ex%3C%2Fmi%3E%3C%2Fmath%3E)
的一元二次方程
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmsup%3E%3Cmrow%3E%3Cmi%3Ex%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsup%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmn%3E3%3C%2Fmn%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmi%3Ek%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmath%3E)
有实数根,则实数
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Ek%3C%2Fmi%3E%3C%2Fmath%3E)
的取值范围是( )
-
8.
我国古代《四元玉鉴》中记载“二果问价”问题,其内容大致如下:用九百九十九文钱,可买甜果苦果共一千个,若
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmtext%3E%E2%8B%AF%3C%2Fmtext%3E%3Cmn%3E%2C%3C%2Fmn%3E%3Cmtext%3E%E2%8B%AF%3C%2Fmtext%3E%3C%2Fmath%3E)
, 试向买甜果苦果各几个?
若设买甜果
个,买苦果
个,可列出符合题意的二元一次方程组:
根据已有信息,题中用“…,…”表示的缺失的条件应为 ( )
A . 甜果七个用四文钱,苦果九个用十一文钱
B . 甜果十一个用九文钱,苦果四个用七文钱
C . 甜果四个用七文钱,苦果十一个用九文钱
D . 甜果九个用十一文钱,苦果七个用四文钱
-
9.
如图,
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmtext%3ER%3C%2Fmtext%3E%3Cmtext%3Et%3C%2Fmtext%3E%3Cmtext%3E%E2%96%B3%3C%2Fmtext%3E%3Cmi%3EA%3C%2Fmi%3E%3Cmi%3EB%3C%2Fmi%3E%3Cmi%3EC%3C%2Fmi%3E%3C%2Fmath%3E)
中,
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmo%3E%E2%88%A0%3C%2Fmo%3E%3Cmi%3EA%3C%2Fmi%3E%3Cmi%3EB%3C%2Fmi%3E%3Cmi%3EC%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E9%3C%2Fmn%3E%3Cmsup%3E%3Cmrow%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmo%3E%C2%B0%3C%2Fmo%3E%3C%2Fmrow%3E%3C%2Fmsup%3E%3C%2Fmath%3E)
, 分别以顶点A,C为圆心,大于
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmfrac%3E%3Cmrow%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmfrac%3E%3Cmi%3EA%3C%2Fmi%3E%3Cmi%3EC%3C%2Fmi%3E%3C%2Fmath%3E)
的长为半径画弧,两弧分别相交于点
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EM%3C%2Fmi%3E%3C%2Fmath%3E)
和点
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EN%3C%2Fmi%3E%3C%2Fmath%3E)
, 作直线MN分别与BC,AC交于点
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EE%3C%2Fmi%3E%3C%2Fmath%3E)
和点
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EF%3C%2Fmi%3E%3C%2Fmath%3E)
;以点
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EA%3C%2Fmi%3E%3C%2Fmath%3E)
为圆心,任意长为半径画弧,分别交AB,AC于点
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EH%3C%2Fmi%3E%3C%2Fmath%3E)
和点
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EG%3C%2Fmi%3E%3C%2Fmath%3E)
, 再分别以点
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EH%3C%2Fmi%3E%3C%2Fmath%3E)
, 点
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EG%3C%2Fmi%3E%3C%2Fmath%3E)
为圆心,大于
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmfrac%3E%3Cmrow%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmfrac%3E%3Cmi%3EH%3C%2Fmi%3E%3Cmi%3EG%3C%2Fmi%3E%3C%2Fmath%3E)
的长为半径画弧、两弧交于点
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EP%3C%2Fmi%3E%3C%2Fmath%3E)
, 作射线AP.若射线AP恰好经过点
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EE%3C%2Fmi%3E%3C%2Fmath%3E)
, 则下列四个结论:①
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmo%3E%E2%88%A0%3C%2Fmo%3E%3Cmi%3EC%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E3%3C%2Fmn%3E%3Cmsup%3E%3Cmrow%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmo%3E%C2%B0%3C%2Fmo%3E%3C%2Fmrow%3E%3C%2Fmsup%3E%3C%2Fmath%3E)
;
②AP垂直平分线段BF;③CE=2BE;④
.
其中,正确结论的个数有 ( )
![](//tikupic.21cnjy.com/2024/07/04/9f/c5/9fc519399be77924778db2e78fd1a643_114x105.png)
A . 1个
B . 2个
C . 3个
D . 4个
-
10.
两个半径相等的半圆按如图方式放置,半圆
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsup%3E%3Cmrow%3E%3Cmi%3EO%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmsup%3E%3Cmi%3E%3C%2Fmi%3E%3Cmn%3E%27%3C%2Fmn%3E%3C%2Fmsup%3E%3C%2Fmrow%3E%3C%2Fmsup%3E%3C%2Fmath%3E)
的一个直径端点与半圆
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EO%3C%2Fmi%3E%3C%2Fmath%3E)
的圆心重合.若半圆的半径为2,则阴影部分的面积是( )
![](//tikupic.21cnjy.com/2024/07/15/dc/03/dc03a68453ae1ab6bc9a1f9869d5cd82.png)
-
11.
如图所示是二次函数
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Ey%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmi%3Ea%3C%2Fmi%3E%3Cmsup%3E%3Cmrow%3E%3Cmi%3Ex%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsup%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmi%3Eb%3C%2Fmi%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmi%3Ec%3C%2Fmi%3E%3Cmn%3E%28%3C%2Fmn%3E%3Cmi%3Ea%3C%2Fmi%3E%3Cmo%3E%E2%89%A0%3C%2Fmo%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmn%3E%29%3C%2Fmn%3E%3C%2Fmath%3E)
的部分图象,该函数图象的对称轴是直线
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmath%3E)
, 图象与
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Ey%3C%2Fmi%3E%3C%2Fmath%3E)
轴交点的纵坐标是2.则下列结论:①2a+b=0;②方程
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Ea%3C%2Fmi%3E%3Cmsup%3E%3Cmrow%3E%3Cmi%3Ex%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsup%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmi%3Eb%3C%2Fmi%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmi%3Ec%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmath%3E)
一定有一个根在-2和-1之间;③方程
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Ea%3C%2Fmi%3E%3Cmsup%3E%3Cmrow%3E%3Cmi%3Ex%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsup%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmi%3Eb%3C%2Fmi%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmi%3Ec%3C%2Fmi%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmfrac%3E%3Cmrow%3E%3Cmn%3E3%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmfrac%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmath%3E)
一定有两个不相等的实数根;④
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Eb%3C%2Fmi%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmi%3Ea%3C%2Fmi%3E%3Cmo%3E%26lt%3B%3C%2Fmo%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmath%3E)
.其中,正确结论的个数有( )
A . 1个
B . 2个
C . 3个
D . 4个
-
12.
如图,菱形ABCD中,
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmo%3E%E2%88%A0%3C%2Fmo%3E%3Cmi%3EB%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E6%3C%2Fmn%3E%3Cmsup%3E%3Cmrow%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmo%3E%C2%B0%3C%2Fmo%3E%3C%2Fmrow%3E%3C%2Fmsup%3E%3C%2Fmath%3E)
, 点
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EE%3C%2Fmi%3E%3C%2Fmath%3E)
是AB边上的点,
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EA%3C%2Fmi%3E%3Cmi%3EE%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E4%3C%2Fmn%3E%3Cmn%3E%2C%3C%2Fmn%3E%3Cmi%3EB%3C%2Fmi%3E%3Cmi%3EE%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E8%3C%2Fmn%3E%3C%2Fmath%3E)
, 点
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EF%3C%2Fmi%3E%3C%2Fmath%3E)
是BC上的一点,
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmtext%3E%E2%96%B3%3C%2Fmtext%3E%3Cmi%3EE%3C%2Fmi%3E%3Cmi%3EG%3C%2Fmi%3E%3Cmi%3EF%3C%2Fmi%3E%3C%2Fmath%3E)
是以点
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EG%3C%2Fmi%3E%3C%2Fmath%3E)
为直角顶点,
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmo%3E%E2%88%A0%3C%2Fmo%3E%3Cmi%3EE%3C%2Fmi%3E%3Cmi%3EF%3C%2Fmi%3E%3Cmi%3EG%3C%2Fmi%3E%3C%2Fmath%3E)
为
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmn%3E3%3C%2Fmn%3E%3Cmsup%3E%3Cmrow%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmo%3E%C2%B0%3C%2Fmo%3E%3C%2Fmrow%3E%3C%2Fmsup%3E%3C%2Fmath%3E)
角的直角三角形,连结AG.当点
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EF%3C%2Fmi%3E%3C%2Fmath%3E)
在直线BC上运动时,线段AG的最小值是( )
![](//tikupic.21cnjy.com/2024/07/15/99/31/993178e60721097446d6512ea8151c7d.png)
A . 2
B .
C .
D . 4
二、填空题(本大题共6小题、满分24分.只要求填写最后结果,每小题填对得4分)
-
13.
单项式
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmn%3E3%3C%2Fmn%3E%3Cmi%3Ea%3C%2Fmi%3E%3Cmsup%3E%3Cmrow%3E%3Cmi%3Eb%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsup%3E%3C%2Fmath%3E)
的次数是
.
-
14.
某学校在4月23日世界读书日举行“书香校园,全员阅读”活动.小明和小颖去学校图书室借阅书籍,小明准备从《西游记》、《骆驼祥子》、《水浒传》中随机选择一本,小颖准备从《西游记》、《骆驼祥子》、《朝花夕拾》中随机选择一本,小明和小颖恰好选中书名相同的书的概率是.
-
15.
在综合实践课上,数学兴趣小组用所学数学知识测量大汶河某河段的宽度.他们在河岸一侧的瞭望台上放飞一只无人机.如图,无人机在河上方距水面高60米的点
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EP%3C%2Fmi%3E%3C%2Fmath%3E)
处测得瞭望台正对岸
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EA%3C%2Fmi%3E%3C%2Fmath%3E)
处的俯角为
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmn%3E5%3C%2Fmn%3E%3Cmsup%3E%3Cmrow%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmo%3E%C2%B0%3C%2Fmo%3E%3C%2Fmrow%3E%3C%2Fmsup%3E%3C%2Fmath%3E)
, 测得瞭望台顶端
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EC%3C%2Fmi%3E%3C%2Fmath%3E)
处的俯角为
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmn%3E6%3C%2Fmn%3E%3Cmn%3E3%3C%2Fmn%3E%3Cmn%3E.%3C%2Fmn%3E%3Cmsup%3E%3Cmrow%3E%3Cmn%3E6%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmo%3E%C2%B0%3C%2Fmo%3E%3C%2Fmrow%3E%3C%2Fmsup%3E%3C%2Fmath%3E)
, 已知瞭望台
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmtext%3EB%3C%2Fmtext%3E%3Cmtext%3EC%3C%2Fmtext%3E%3C%2Fmath%3E)
高12米(图中点A,B,C,P在同一平面内).那么大汶河此河段的宽AB为
米.(参考数据:
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmn%3Es%3C%2Fmn%3E%3Cmn%3Ei%3C%2Fmn%3E%3Cmn%3En%3C%2Fmn%3E%3Cmn%3E4%3C%2Fmn%3E%3Cmsup%3E%3Cmrow%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmo%3E%C2%B0%3C%2Fmo%3E%3C%2Fmrow%3E%3C%2Fmsup%3E%3Cmo%3E%E2%89%88%3C%2Fmo%3E%3Cmfrac%3E%3Cmrow%3E%3Cmn%3E3%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E5%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmfrac%3E%3Cmn%3E%2C%3C%2Fmn%3E%3Cmn%3Es%3C%2Fmn%3E%3Cmn%3Ei%3C%2Fmn%3E%3Cmn%3En%3C%2Fmn%3E%3Cmn%3E6%3C%2Fmn%3E%3Cmn%3E3%3C%2Fmn%3E%3Cmn%3E.%3C%2Fmn%3E%3Cmsup%3E%3Cmrow%3E%3Cmn%3E6%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmo%3E%C2%B0%3C%2Fmo%3E%3C%2Fmrow%3E%3C%2Fmsup%3E%3Cmo%3E%E2%89%88%3C%2Fmo%3E%3Cmfrac%3E%3Cmrow%3E%3Cmn%3E9%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmfrac%3E%3Cmn%3E%2C%3C%2Fmn%3E%3Cmn%3Et%3C%2Fmn%3E%3Cmn%3Ea%3C%2Fmn%3E%3Cmn%3En%3C%2Fmn%3E%3Cmn%3E5%3C%2Fmn%3E%3Cmsup%3E%3Cmrow%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmo%3E%C2%B0%3C%2Fmo%3E%3C%2Fmrow%3E%3C%2Fmsup%3E%3Cmo%3E%E2%89%88%3C%2Fmo%3E%3Cmfrac%3E%3Cmrow%3E%3Cmn%3E6%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E5%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmfrac%3E%3Cmn%3E%2C%3C%2Fmn%3E%3Cmn%3Et%3C%2Fmn%3E%3Cmn%3Ea%3C%2Fmn%3E%3Cmn%3En%3C%2Fmn%3E%3Cmn%3E6%3C%2Fmn%3E%3Cmn%3E3%3C%2Fmn%3E%3Cmn%3E.%3C%2Fmn%3E%3Cmsup%3E%3Cmrow%3E%3Cmn%3E6%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmo%3E%C2%B0%3C%2Fmo%3E%3C%2Fmrow%3E%3C%2Fmsup%3E%3Cmo%3E%E2%89%88%3C%2Fmo%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmath%3E)
)
![](//tikupic.21cnjy.com/2024/07/04/e9/5c/e95c7fcdabf2bb6b3532b2d96622078f.png)
-
16.
如图,小明的父亲想用长为60米的栅栏,再借助房屋的外墙围成一个矩形的菜园.已知房屋外墙长40米,则可围成的菜园的最大面积是
平方米.
![](//tikupic.21cnjy.com/2024/07/04/44/fb/44fb11c6962a854b6414e0b3be4c8a94.png)
-
17.
如图,AB是
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmtext%3E%E2%8A%99%3C%2Fmtext%3E%3Cmi%3EO%3C%2Fmi%3E%3C%2Fmath%3E)
的直径,AH是
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmtext%3E%E2%8A%99%3C%2Fmtext%3E%3Cmi%3EO%3C%2Fmi%3E%3C%2Fmath%3E)
的切线,点
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EC%3C%2Fmi%3E%3C%2Fmath%3E)
为
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmtext%3E%E2%8A%99%3C%2Fmtext%3E%3Cmi%3EO%3C%2Fmi%3E%3C%2Fmath%3E)
上任意一点,点
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3ED%3C%2Fmi%3E%3C%2Fmath%3E)
为
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmover+accent%3D%22true%22%3E%3Cmrow%3E%3Cmi%3EA%3C%2Fmi%3E%3Cmi%3EC%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmo+stretchy%3D%22true%22%3E%E2%8C%A2%3C%2Fmo%3E%3C%2Fmover%3E%3C%2Fmath%3E)
的中点,连结BD交AC于点
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EE%3C%2Fmi%3E%3C%2Fmath%3E)
, 延长BD与AH相交于点
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EF%3C%2Fmi%3E%3C%2Fmath%3E)
.若
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3ED%3C%2Fmi%3E%3Cmi%3EF%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmn%3E%2C%3C%2Fmn%3E%3Cmn%3Et%3C%2Fmn%3E%3Cmn%3Ea%3C%2Fmn%3E%3Cmn%3En%3C%2Fmn%3E%3Cmi%3EB%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmfrac%3E%3Cmrow%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmfrac%3E%3C%2Fmath%3E)
, 则AE的长为
.
![](//tikupic.21cnjy.com/2024/07/04/d7/1f/d71fd24b3a0857b2e06509e25f8ed16c.png)
-
18.
如图所示,是用图形“○”和“●”按一定规律摆成的“小屋子”.
![](//tikupic.21cnjy.com/2024/07/04/a9/d9/a9d9d8cf3691febb98243992db7d2316.png)
按照此规律继续摆下去,第个“小屋子”中图形“○”个数是图形“●”个数的3倍.
三、解答题(本大题共7小题,满分78分.解答应写出必要的文字说明、证明过程或推演步骤)
-
19.
-
(1)
计算:
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmn%3Et%3C%2Fmn%3E%3Cmn%3Ea%3C%2Fmn%3E%3Cmn%3En%3C%2Fmn%3E%3Cmn%3E6%3C%2Fmn%3E%3Cmsup%3E%3Cmrow%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmo%3E%C2%B0%3C%2Fmo%3E%3C%2Fmrow%3E%3C%2Fmsup%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmsup%3E%3Cmrow%3E%3Cmrow%3E%3Cmo%3E%28%3C%2Fmo%3E%3Cmrow%3E%3Cmfrac%3E%3Cmrow%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmfrac%3E%3C%2Fmrow%3E%3Cmo%3E%29%3C%2Fmo%3E%3C%2Fmrow%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsup%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmn%3E%7C%3C%2Fmn%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmsqrt%3E%3Cmrow%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsqrt%3E%3Cmn%3E%7C%3C%2Fmn%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmsqrt%3E%3Cmrow%3E%3Cmn%3E%28%3C%2Fmn%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmn%3E3%3C%2Fmn%3E%3Cmsup%3E%3Cmrow%3E%3Cmn%3E%29%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsup%3E%3C%2Fmrow%3E%3C%2Fmsqrt%3E%3C%2Fmath%3E)
;
-
(2)
化简:
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmo%3E%28%3C%2Fmo%3E%3Cmrow%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmfrac%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmi%3Ex%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmfrac%3E%3C%2Fmrow%3E%3Cmo%3E%29%3C%2Fmo%3E%3C%2Fmrow%3E%3Cmo%3E%C3%B7%3C%2Fmo%3E%3Cmfrac%3E%3Cmrow%3E%3Cmsup%3E%3Cmrow%3E%3Cmi%3Ex%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsup%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmi%3Ex%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmfrac%3E%3C%2Fmath%3E)
.
-
20.
某超市打算购进一批苹果.现从甲、乙两个供应商供应的苹果中各随机抽取10个,测得它们的直径(单位:
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmtext%3Em%3C%2Fmtext%3E%3Cmtext%3Em%3C%2Fmtext%3E%3C%2Fmath%3E)
),并制作统计图如下:
![](//tikupic.21cnjy.com/2024/07/04/4a/07/4a077e91ec08125a12471c07961388a1.png)
根据以上信息,解答下列问题:
-
(1)
统计量 供应商 | 平均数 | 中位数 | 众数 |
甲 | 80 | 80 | b |
乙 | m | a | 76 |
则
,
,b=.
-
(2)
苹果直径的方差越小,苹果的大小越整齐,据此判断,供应商供应的苹果大小更为整齐。(填“甲”或“乙”)
-
(3)
超市规定直径
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmn%3E8%3C%2Fmn%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmtext%3Em%3C%2Fmtext%3E%3Cmtext%3Em%3C%2Fmtext%3E%3C%2Fmath%3E)
(含
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmn%3E8%3C%2Fmn%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmtext%3Em%3C%2Fmtext%3E%3Cmtext%3Em%3C%2Fmtext%3E%3C%2Fmath%3E)
)以上的苹果为大果.超市打算购进甲供应商的苹果2000个,其中,大果约有多少个?
-
21.
直线
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3Ey%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmi%3Ek%3C%2Fmi%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmi%3Eb%3C%2Fmi%3E%3Cmn%3E%28%3C%2Fmn%3E%3Cmi%3Ek%3C%2Fmi%3E%3Cmo%3E%E2%89%A0%3C%2Fmo%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmn%3E%29%3C%2Fmn%3E%3C%2Fmath%3E)
与反比例函数
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3Ey%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmfrac%3E%3Cmrow%3E%3Cmn%3E8%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmi%3Ex%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmfrac%3E%3C%2Fmath%3E)
的图像相交于点
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EA%3C%2Fmi%3E%3Cmn%3E%28%3C%2Fmn%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmn%3E%2C%3C%2Fmn%3E%3Cmi%3Em%3C%2Fmi%3E%3Cmn%3E%29%3C%2Fmn%3E%3Cmn%3E%2C%3C%2Fmn%3E%3Cmi%3EB%3C%2Fmi%3E%3Cmn%3E%28%3C%2Fmn%3E%3Cmi%3En%3C%2Fmi%3E%3Cmn%3E%2C%3C%2Fmn%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmn%3E%29%3C%2Fmn%3E%3C%2Fmath%3E)
, 与
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Ey%3C%2Fmi%3E%3C%2Fmath%3E)
轴交于点
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EC%3C%2Fmi%3E%3C%2Fmath%3E)
.
![](//tikupic.21cnjy.com/2024/07/04/37/76/3776d59334fec51ff3544833c58e4b11.png)
-
(1)
求直线
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3Ey%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3C%2Fmath%3E)
的表达式;
-
(2)
若
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3Ey%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3Cmo%3E%26gt%3B%3C%2Fmo%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3Ey%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3C%2Fmath%3E)
, 请直接写出满足条件的
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Ex%3C%2Fmi%3E%3C%2Fmath%3E)
的取值范围;
-
(3)
过
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EC%3C%2Fmi%3E%3C%2Fmath%3E)
点作
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Ex%3C%2Fmi%3E%3C%2Fmath%3E)
轴的平行线交反比例函数的图象于点
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3ED%3C%2Fmi%3E%3C%2Fmath%3E)
, 求
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmtext%3E%E2%96%B3%3C%2Fmtext%3E%3Cmi%3EA%3C%2Fmi%3E%3Cmi%3EC%3C%2Fmi%3E%3Cmi%3ED%3C%2Fmi%3E%3C%2Fmath%3E)
的面积.
-
22.
随着快递行业的快速发展,全国各地的农产品有了更广阔的销售空间.某农产品加工企业有甲、乙两个组共35名工人.甲组每天加工3000件农产品,乙组每天加工2700件农产品.已知乙组每人每天平均加工的农产品数量是甲组每人每天平均加工农产品数量的1.2倍.求甲、乙两组各有多少名工人?
-
23.
综合与实践
为了研究折纸过程蕴含的数学知识,某校九年级数学兴趣小组的同学进行了数学折纸探究活动.
![](//tikupic.21cnjy.com/2024/07/04/c0/6d/c06d3cb92b0f971d4e178ea0c8a77174_444x183.png)
-
(1)
【探索发现】
同学们对一张矩形纸片进行折叠,如图1,把矩形纸片ABCD翻折,使矩形顶点
的对应点
恰好落在矩形的一边CD上,折痕为EF,将纸片展平,连结BG.EF与BG相交于点H.同学们发现图形中四条线段成比例,即
, 请你判断同学们的发现是否正确,并说明理由.
-
-
24.
如图1,在等腰Rt
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmtext%3E%E2%96%B3%3C%2Fmtext%3E%3Cmi%3EA%3C%2Fmi%3E%3Cmi%3EB%3C%2Fmi%3E%3Cmi%3EC%3C%2Fmi%3E%3C%2Fmath%3E)
中,
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmo%3E%E2%88%A0%3C%2Fmo%3E%3Cmi%3EA%3C%2Fmi%3E%3Cmi%3EB%3C%2Fmi%3E%3Cmi%3EC%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E9%3C%2Fmn%3E%3Cmsup%3E%3Cmrow%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmo%3E%C2%B0%3C%2Fmo%3E%3C%2Fmrow%3E%3C%2Fmsup%3E%3Cmn%3E%2C%3C%2Fmn%3E%3Cmi%3EA%3C%2Fmi%3E%3Cmi%3EB%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmi%3EC%3C%2Fmi%3E%3Cmi%3EB%3C%2Fmi%3E%3C%2Fmath%3E)
, 点D,E分别在AB,CB上,
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3ED%3C%2Fmi%3E%3Cmi%3EB%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmi%3EE%3C%2Fmi%3E%3Cmi%3EB%3C%2Fmi%3E%3C%2Fmath%3E)
、连结AE,CD,取AE中点
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EF%3C%2Fmi%3E%3C%2Fmath%3E)
, 连结BF.
![](//tikupic.21cnjy.com/2024/07/04/89/02/8902e41aa3ce97b43643e39beefbf118_341x160.png)
-
-
(2)
将△DBE绕点
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EB%3C%2Fmi%3E%3C%2Fmath%3E)
顺时针旋转到图2的位置.
①请直接写出BF与CD的位置关系;
②求证:
.
-
25.
如图,抛物线
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3EC%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3Cmn%3E%3A%3C%2Fmn%3E%3Cmi%3Ey%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmi%3Ea%3C%2Fmi%3E%3Cmsup%3E%3Cmrow%3E%3Cmi%3Ex%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsup%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmfrac%3E%3Cmrow%3E%3Cmn%3E4%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E3%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmfrac%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmn%3E4%3C%2Fmn%3E%3C%2Fmath%3E)
的图象经过点
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3ED%3C%2Fmi%3E%3Cmn%3E%28%3C%2Fmn%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmn%3E%2C%3C%2Fmn%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmn%3E%29%3C%2Fmn%3E%3C%2Fmath%3E)
, 与
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Ex%3C%2Fmi%3E%3C%2Fmath%3E)
轴交于点
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EA%3C%2Fmi%3E%3C%2Fmath%3E)
, 点
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EB%3C%2Fmi%3E%3C%2Fmath%3E)
.
![](//tikupic.21cnjy.com/2024/07/04/8f/83/8f83e3c248482197163317f4849173a0_450x246.png)
-
(1)
求抛物线
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3EC%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3C%2Fmath%3E)
的表达式;
-
(2)
将拋物线
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3EC%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3C%2Fmath%3E)
向右平移1个单位,再向上平移3个单位得到拋物线
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3EC%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3C%2Fmath%3E)
, 求拋物线
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3EC%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3C%2Fmath%3E)
的表达式,并判断点
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3ED%3C%2Fmi%3E%3C%2Fmath%3E)
是否在拋物线
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3EC%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3C%2Fmath%3E)
上;
-
(3)
在
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Ex%3C%2Fmi%3E%3C%2Fmath%3E)
轴上方的抛物线
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3EC%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3C%2Fmath%3E)
上,是否存在点
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EP%3C%2Fmi%3E%3C%2Fmath%3E)
, 使
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmtext%3E%E2%96%B3%3C%2Fmtext%3E%3Cmi%3EP%3C%2Fmi%3E%3Cmi%3EB%3C%2Fmi%3E%3Cmi%3ED%3C%2Fmi%3E%3C%2Fmath%3E)
是等腰直角三角形.若存在,请求出点
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EP%3C%2Fmi%3E%3C%2Fmath%3E)
的坐标;若不存在,请说明理由.