一、<table border=0 cellspacing=0 cellpadding=0 > <tr > <td > <p><b >单选题</b></p> </td> </tr> </table>
-
1.
抛物线
![](//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%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmsup%3E%3Cmrow%3E%3Cmrow%3E%3Cmo%3E%28%3C%2Fmo%3E%3Cmrow%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmo%3E%29%3C%2Fmo%3E%3C%2Fmrow%3E%3C%2Fmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmsup%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmn%3E3%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
的顶点坐标是( )
A . (2,3)
B . (-2,3)
C . (2,-3)
D . (-2,-3)
-
2.
将两个全等的直角三角形纸片构成如图的四个图形,其中属于中心对称图形的是( )
-
3.
如图,⊙O是△ABC的外接圆,若AB=OA=OB,则∠C等于( )
![](//tikupic.21cnjy.com/26/e0/26e004468b73a959f00687f47b3e8b59.png)
A . 30°
B . 40°
C . 60°
D . 80°
-
4.
方程
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmsup%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmsup%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmn%3E3%3C%2Fmn%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmn%3E5%3C%2Fmn%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
的根的情况是( )
A . 有两个不相等的实数根
B . 有两个相等的实数根
C . 没有实数根
D . 无法确定是否有实数根
-
5.
在一个不透明的盒子里装有3个黑球和1个白球,每个球除颜色外都相同,从中任意摸出2个球,下列事件中,不可能事件是( )
A . 摸出的2个球有一个是白球
B . 摸出的2个球都是黑球
C . 摸出的2个球有一个黑球
D . 摸出的2个球都是白球
-
6.
已知点
![](//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%3Cmo+stretchy%3D%22false%22%3E%28%3C%2Fmo%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmo%3E++%EF%BC%8C+%3C%2Fmo%3E%3Cmsub%3E%3Cmi%3Ey%3C%2Fmi%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmsub%3E%3Cmo+stretchy%3D%22false%22%3E%29%3C%2Fmo%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
,
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmi%3EB%3C%2Fmi%3E%3Cmo+stretchy%3D%22false%22%3E%28%3C%2Fmo%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmo%3E++%EF%BC%8C+%3C%2Fmo%3E%3Cmsub%3E%3Cmi%3Ey%3C%2Fmi%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmsub%3E%3Cmo+stretchy%3D%22false%22%3E%29%3C%2Fmo%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
是反比例函数
![](//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%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmfrac%3E%3Cmn%3E5%3C%2Fmn%3E%3Cmi%3Ex%3C%2Fmi%3E%3C%2Fmfrac%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
的图像上的两点,下列结论正确的是( )
-
7.
已知点
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmsub%3E%3Cmi%3EP%3C%2Fmi%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmsub%3E%3Cmo+stretchy%3D%22false%22%3E%28%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmo%3E%2C%3C%2Fmo%3E%3Cmn%3E3%3C%2Fmn%3E%3Cmo+stretchy%3D%22false%22%3E%29%3C%2Fmo%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
,它关于原点的对称点是点
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmsub%3E%3Cmi%3EP%3C%2Fmi%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmsub%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
,则点
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmsub%3E%3Cmi%3EP%3C%2Fmi%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmsub%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
的坐标是( )
A . (3,1)
B . (1,-3)
C . (-1,-3)
D . (-3,-1)
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8.
如图所示,边长为2的正三角形ABO的边OB在x轴上,将△ABO绕原点O逆时针旋转30°得到三角形OA
1B
1 , 则点A
1的坐标为( )
![](//tikupic.21cnjy.com/71/2f/712f59c2877de179936558abbd77daeb.png)
A . (
,1)
B . (
,-1)
C . (-1,
)
D . (2,1)
-
9.
如图,在平面直角坐标系中,点A、B均在函数
![](//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%3Ek%3C%2Fmi%3E%3Cmi%3Ex%3C%2Fmi%3E%3C%2Fmfrac%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
(k>0,x>0)的图象上,⊙A与x轴相切,⊙B与y轴相切.若点B的坐标为(1,6),⊙A的半径是⊙B的半径的2倍,则点A的坐标为( )
![](//tikupic.21cnjy.com/46/4c/464cb2a407be2b07de0ab46141c933f1.png)
A . (2,2)
B . (2,3)
C . (3, 2)
D . (4,
)
-
10.
已知函数
![](//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%3Cmn%3E4%3C%2Fmn%3E%3Cmsup%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmsup%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmn%3E4%3C%2Fmn%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmi%3Em%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
的图像与x轴的交点坐标为
![](//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%3Cmsub%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmsub%3E%3Cmo%3E++%EF%BC%8C+%3C%2Fmo%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmo+stretchy%3D%22false%22%3E%29%3C%2Fmo%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
且
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmrow%3E%3Cmo%3E%28%3C%2Fmo%3E%3Cmrow%3E%3Cmsub%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmsub%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmsub%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmsub%3E%3C%2Fmrow%3E%3Cmo%3E%29%3C%2Fmo%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmo%3E%28%3C%2Fmo%3E%3Cmrow%3E%3Cmn%3E4%3C%2Fmn%3E%3Cmsubsup%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmsubsup%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmn%3E5%3C%2Fmn%3E%3Cmsub%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmsub%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmsub%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmsub%3E%3C%2Fmrow%3E%3Cmo%3E%29%3C%2Fmo%3E%3C%2Fmrow%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E8%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
,则该函数的最小值是( )
A . 2
B . -2
C . 10
D . -10
二、<table border=0 cellspacing=0 cellpadding=0 > <tr > <td > <p><b >填空题</b></p> </td> </tr> </table>
-
11.
若函数
![](//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%3Cmrow%3E%3Cmi%3Em%3C%2Fmi%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmi%3Ex%3C%2Fmi%3E%3C%2Fmfrac%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
,当
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E%26gt%3B%3C%2Fmo%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
时,函数值y随自变量x的增大而减少,则m的取值范围是
.
-
12.
从点A(-2,4)、B(-2,-4)、C(1,-8)中任取一个点,则该点在
![](//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%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmfrac%3E%3Cmn%3E8%3C%2Fmn%3E%3Cmi%3Ex%3C%2Fmi%3E%3C%2Fmfrac%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
的图像上的概率是
.
-
-
14.
若将抛物线y=x2-4x-3的图像向右平移3个单位,则所得抛物线的解析式是.
-
15.
一个圆锥的侧面展开图是半径为1的半圆,则该圆锥的底面半径是
.
![](//tikupic.21cnjy.com/8d/3d/8d3de5912cead619fc4bffff57a3e84f.png)
-
16.
如图是二次函数y=ax
2+bx+c的部分图像 ,在下列四个结论中正确的是
.
①不等式ax2+bx+c>0的解集是-1<x<5;②a-b+c>0;③b2-4ac>0;④4a+b<0.
![](//tikupic.21cnjy.com/6b/e9/6be91540a3ef0fe97b436dca243a2658.png)
三、<table border=0 cellspacing=0 cellpadding=0 > <tr > <td > <p><b >解答题</b></p> </td> </tr> </table>
-
17.
解方程:
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmsup%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmsup%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmn%3E5%3C%2Fmn%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
.
-
18.
如图,AB是⊙O的一条弦,OD⊥AB,垂足为C,交⊙O于点D,点E在⊙O上.
![](//tikupic.21cnjy.com/de/19/de197edded4f210d6c602dfde62c5a96.png)
-
-
-
19.
如图,正方形ABCD的边长为2,E是BC的中点,以点A为中心,把△ABE绕点A顺时针旋转90°,设点E的对应点为F.
![](//tikupic.21cnjy.com/0b/82/0b8208e13a090a14971281745372785e.png)
-
(1)
画出旋转后的三角形.(尺规作图,保留作图痕迹,不写作法)
-
-
20.
(2017·苏州模拟)
甲、乙、丙、丁四位同学进行一次乒乓球单打比赛,要从中选出两位同学打第一场比赛.
-
(1)
若已确定甲打第一场,再从其余三位同学中随机选取一位,求恰好选中乙同学的概率.
-
(2)
请用树状图法或列表法,求恰好选中甲、乙两位同学的概率.
-
21.
某工厂生产的某种产品按质量分为10个档次,第1档次(最低档次)的产品一天能生产95件,每件利润6元.每提高一个档次,每件利润增加2元,但一天产量减少5件.
-
(1)
若生产第x档次的产品一天的总利润为y元(其中x为正整数,且1≤x≤10),求出y关于x的函数关系式;
-
(2)
若生产第x档次的产品一天的总利润为1120元,求该产品的质量档次.
-
22.
如图所示,AB为半圆O的直径,C为圆上一点,AD平分∠BAC交半圆于点D,过点D作DE⊥AC,DE交AC的延长线于点E.
![](//tikupic.21cnjy.com/94/3a/943afd2176423424a2fb1468345c4adf.png)
-
-
(2)
若⊙O的半径为2,DE=
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmsqrt%3E%3Cmn%3E3%3C%2Fmn%3E%3C%2Fmsqrt%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
,求线段AC的长
-
23.
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%3Ek%3C%2Fmi%3E%3Cmi%3Ex%3C%2Fmi%3E%3C%2Fmfrac%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
在第一象限的图象如图所示,过点A(1,0)作x轴的垂线,交反比例函数
![](//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%3Ek%3C%2Fmi%3E%3Cmi%3Ex%3C%2Fmi%3E%3C%2Fmfrac%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
的图象于点M,△AOM的面积为3.
![](//tikupic.21cnjy.com/58/5f/585f5470582ed9f46dfb997d3f3f969b.png)
-
-
(2)
设点B的坐标为(t,0),其中t>1.若以AB为一边的正方形有一个顶点在反比例函数
![](//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%3Ek%3C%2Fmi%3E%3Cmi%3Ex%3C%2Fmi%3E%3C%2Fmfrac%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
的图象上,求t的值.
-
24.
如图1,已知矩形ABCD的宽AD=8,点E在边AB上,P为线段DE上的一动点(点P与点D,E不重合),∠MPN=90°,M,N分别在直线AB,CD上,过点P作直线HK
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmo%3E%2F%3C%2Fmo%3E%3Cmo%3E%2F%3C%2Fmo%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
AB,作PF⊥AB,垂足为点F,过点N作NG⊥HK,垂足为点G
![](//tikupic.21cnjy.com/2d/64/2d645943ea5f48f4a4ecb4dae1bda3f3.png)
-
-
(2)
在图1中,将直角∠MPN绕点P顺时针旋转,在这一过程中,试观察、猜想:当MF=NG时,△MPN是什么特殊三角形?在图2中用直尺画出图形,并证明你的猜想;
![](//tikupic.21cnjy.com/f1/92/f19249aef2054e856001c8e649e125ad.png)
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(3)
在(2)的条件下,当∠EDC=30°时,设EP=x,△MPN的面积为S,求出S关于x的解析式,并说明S是否存在最小值?若存在,求出此时x的值和△MPN面积的最小值;若不存在,请说明理由。
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25.
如图,已知抛物线
![](//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%3Cmn%3E1%3C%2Fmn%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmfrac%3E%3Cmsup%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmsup%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmi%3Ea%3C%2Fmi%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmn%3E4%3C%2Fmn%3E%3Cmi%3Ea%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
与x轴交于点A,B,与y轴负半轴交于点C且OB=OC,点P为抛物线上的一个动点,且点P位于x轴下方,点P与点C不重合。
![](//tikupic.21cnjy.com/16/97/1697acbbace27c10b9fb3135b8006b30.png)
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(2)
若△PAC的面积为
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmfrac%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmfrac%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
,求点P的坐标
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(3)
若以A、B、C、P为顶点的四边形面积记作S,则S取何值时,对应的点P有且只有2个?