一、选择题(本题有10小题,每小题4分,共40分.)
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1.
2022年新能源车企迎来了更多的关注,如图是四款新能源汽车的标志,是中心对称图形的是( )
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3.
如果反比例函数
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmi%3Ey%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmfrac%3E%3Cmi%3Ea%3C%2Fmi%3E%3Cmi%3Ex%3C%2Fmi%3E%3C%2Fmfrac%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
的图象分布在第一、三象限,那么a的值可以是( )
A . -3
B . 2
C . 0
D . -2
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A . 明天会下雨
B . 任意画一个三角形,其内角和为
C . 抛一枚硬币,正面朝上
D . 打开电视机,正在播放广告
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5.
如图,在平面直角坐标系中,将点A(3,2)绕原点O逆时针旋转90°得到点B,则点B的坐标为( )
![](//tikupic.21cnjy.com/2023/02/09/93/2d/932d33f153b963da69801f2d525dd9d6.png)
A . (-2,3)
B . (-3,2)
C . (-2,-3)
D . (-1,3)
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6.
二次函数
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmi%3Ey%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmi%3Ea%3C%2Fmi%3E%3Cmsup%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmsup%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmi%3Eb%3C%2Fmi%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmn%3E5%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
与x轴交于(1,0)、(-3,0),则关于x的方程
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmi%3Ea%3C%2Fmi%3E%3Cmsup%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmsup%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmi%3Eb%3C%2Fmi%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E5%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
的解为( )
A . 1,3
B . 1,-5
C . -1,3
D . 1,-3
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7.
有一人患了流感,经过两轮传染后共有121人患了流感,每轮传染中平均一个人传染了几个人?设每轮传染中平均一个人传染了x个人,下列所列方程正确的是( )
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8.
如图,已知点A、点C在⊙O上,AB是⊙O切线,连接AC,若∠ACO=65°,则∠CAB的度数为( )
![](//tikupic.21cnjy.com/2023/03/14/d9/51/d951ccbe0f0803b77ed469a830ccdd5b_m_209x155.png)
A . 35°
B . 30°
C . 25°
D . 20°
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9.
如图,Rt△ABC中,∠ACB=90°,BC=4,AC=3,将△ABC绕点B逆时针旋转得
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmo%3E%E2%96%B3%3C%2Fmo%3E%3Cmsup%3E%3Cmi%3EA%3C%2Fmi%3E%3Cmn%3E%27%3C%2Fmn%3E%3C%2Fmsup%3E%3Cmi%3EB%3C%2Fmi%3E%3Cmsup%3E%3Cmi%3EC%3C%2Fmi%3E%3Cmn%3E%27%3C%2Fmn%3E%3C%2Fmsup%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
, 若点
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsup%3E%3Cmi%3EC%3C%2Fmi%3E%3Cmn%3E%27%3C%2Fmn%3E%3C%2Fmsup%3E%3C%2Fmath%3E)
在AB上,则
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmi%3EA%3C%2Fmi%3E%3Cmsup%3E%3Cmi%3EA%3C%2Fmi%3E%3Cmn%3E%27%3C%2Fmn%3E%3C%2Fmsup%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
的长为( )
![](//tikupic.21cnjy.com/2023/02/09/ec/34/ec34e22bb4d488b31114fa7b33f0a70f.png)
A .
B . 4
C .
D . 5
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二、填空题(本题有6小题,每小题5分,共30分).
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11.
点
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmo+stretchy%3D%22false%22%3E%28%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmo%3E++%EF%BC%8C+%3C%2Fmo%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmn%3E5%3C%2Fmn%3E%3Cmo+stretchy%3D%22false%22%3E%29%3C%2Fmo%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
关于原点对称的点的坐标为
.
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12.
某射击运动员封闭训练10个月,每天击中9环以上的频率记录如下图,封闭训练结束时,估计这名运动员射击一次时“击中9环以上”的概率为
(结果保留一位小数).
![](//tikupic.21cnjy.com/2023/02/09/7f/76/7f76c61e515b24c4857d06baed6d686e.png)
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14.
如图,已知
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmover+accent%3D%22true%22%3E%3Cmrow%3E%3Cmi%3EA%3C%2Fmi%3E%3Cmi%3EB%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmo+stretchy%3D%22true%22%3E%E2%8C%A2%3C%2Fmo%3E%3C%2Fmover%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
与
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmover+accent%3D%22true%22%3E%3Cmrow%3E%3Cmi%3EC%3C%2Fmi%3E%3Cmi%3ED%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmo+stretchy%3D%22true%22%3E%E2%8C%A2%3C%2Fmo%3E%3C%2Fmover%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
是公路弯道的外、内边线,它们有共同的圆心
![](//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)
, 所对的圆心角都是
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmn%3E72%3C%2Fmn%3E%3Cmo%3E%C2%B0%3C%2Fmo%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
、A、C、O在同一直线上,公路宽
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmi%3EA%3C%2Fmi%3E%3Cmi%3EC%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E20%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
米,则弯道外侧边线比内侧边线多
米(结果保留
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3E%CF%80%3C%2Fmi%3E%3C%2Fmath%3E)
).
![](//tikupic.21cnjy.com/2023/02/01/81/15/8115355156dd30392821b9e537d9a684_122x118.png)
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16.
如图,把双曲线
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmi%3Ey%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmfrac%3E%3Cmi%3Ek%3C%2Fmi%3E%3Cmi%3Ex%3C%2Fmi%3E%3C%2Fmfrac%3E%3Cmo+stretchy%3D%22false%22%3E%28%3C%2Fmo%3E%3Cmi%3Ek%3C%2Fmi%3E%3Cmo%3E%26gt%3B%3C%2Fmo%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmo%3E++%EF%BC%8C+%3C%2Fmo%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E%26gt%3B%3C%2Fmo%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmo+stretchy%3D%22false%22%3E%29%3C%2Fmo%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
绕着原点逆时针旋转
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmn%3E45%3C%2Fmn%3E%3Cmo%3E%C2%B0%3C%2Fmo%3E%3C%2Fmrow%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%3EB%3C%2Fmi%3E%3C%2Fmath%3E)
,
![](//tikupic.21cnjy.com/2023/03/14/13/8f/138f704115ffb6266c21a5cb1e759e94_m_161x122.png)
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(2)
若点A(3,5)在旋转后的曲线上,则k=.
三、解答题(第17~20题,每题8分,第21题10分,第22-23题,每题12分,第24题14分,共80分)
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18.
已知蓄电池的电压为定值,使用蓄电池时,电流I(单位:A)与电阻R(单位:Ω)是反比例函数关系,它的图象如图所示.
![](//tikupic.21cnjy.com/2023/02/01/50/25/5025054f4474ebd5d3e0369bd2ff06cd_173x120.png)
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(1)
求这个反比例函数的解析式,并直接写出蓄电池的电压值(单位:v)
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(2)
如果以此蓄电池为电源的用电器的限制电流不能超过10A,那么用电器可变电阻应控制在什么范围?
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19.
象棋比赛中,采用翻扑克牌比大小的方式决定哪方先走子,五张扑克牌点数分别是1、2、3、4、5,背面无差别,将扑克牌背面朝上,由参赛棋手中一方先翻出一张,然后另一方翻剩下的四张中的一张,点数大者先走;
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(2)
两轮比赛,假设棋手甲翻出点数都是3,求两轮都是甲先走的概率(用画树状图或列表的方法求解)。
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20.
如图,已知一抛物线形大门,其地面宽度为10m,一身高为1.8m的同学站在门内,在离门脚1m处垂直地面站直拍照,其头顶恰好顶在抛物线形门上,根据这些条件,请你求出该大门的高h.
![](//tikupic.21cnjy.com/2023/02/01/2b/31/2b3134978973e7c757c25746fe978ccf_190x106.png)
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21.
如图,是由边长为1的小正方形构成的6×6网格,每个小正方形的顶点叫做格点,⊙O经过A、B、C、D四个格点,
仅用无刻度的直尺在给定的网格中按要求画图(画图过程中起辅助作用的用虚线表示,画图结果用实线表示,并用黑色水笔描黑)
![](//tikupic.21cnjy.com/2023/02/01/b4/9f/b49fb98ebae9f41b140e3d5248a56fb0_478x154.png)
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(1)
如图1,判断圆心O▲ (填“是”或“不是”)在格点上,并在图1中标出格点O;
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(3)
在图2中画出
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmover+accent%3D%22true%22%3E%3Cmrow%3E%3Cmi%3EB%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%2Fmrow%3E%3C%2Fmath%3E)
的中点E;
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22.
如图,将△ABC绕点A顺时针旋转得到△AED,并使C点的对应点D点落在直线BC上,
![](//tikupic.21cnjy.com/2023/02/01/dd/01/dd013e232216bda978f4f980da22de3e_574x139.png)
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(2)
如图2,AE与BD交于点F,若∠AFB=50°,∠B=20°,求∠BAC的度数;
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(3)
如图3,连接BE,若EB=13,ED=5,CD=17,则AD的长为.
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23.
如图1,小球从倾斜轨道AB由静止滚下时,经过的路程s(米)与时间t(秒)的部分数据如下表.
t(秒)
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0
|
0.4
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0.8
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1
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1.2
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1.6
|
…
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s(米)
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0
|
0.016
|
0.064
|
0.1
|
0.144
|
0.256
|
…
|
![](//tikupic.21cnjy.com/2023/02/01/6c/81/6c811c5c647b6df5044dcbdcdc04deed_415x124.png)
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(1)
请在一次函数、二次函数、反比例函数中选择最适合s与t的函数类型,并求出解析式;
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(3)
如图2,与轨道AB相连的是一段水平光滑轨道BC,BC的另一端连接的是与AB平行的轨道CD,CD足够长。两个同样的小球甲与乙分别从A、C处同时静止滚下,其中甲球在BC上滚动的时间是2秒,速度是0.4米/秒,问总运动时间为多少时,两球滚过的路程差为1.6米?
(注:小球大小忽略不计,小球在下一段轨道的开始速度等于它在上一段轨道的最后速度)
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24.
如图⊙O半径为r,锐角△ABC内接于⊙O,连AO并延长交BC于D,过点D作DE⊥AC于E.
![](//tikupic.21cnjy.com/2023/02/01/46/6a/466a58f48c3fd44f8b04273dd76d325d_388x131.png)
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(2)
如图1,若CD=OA,AB=6,求DE的长;
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(3)
如图2,当∠DAC=2∠DAB时,BD=5,DC=6,求r的值;
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(4)
如图3,若AE=AB=BD=1,直接写出AD+DE的值(用含r的代数式表示)