一、</strong><strong>选择题</strong><strong>(本大题共8小题,每小题4分,共32分,答案涂在答题卡上)</strong>
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2.
若x>y , 则下列各式正确的是( )
A . x+2<y+2
B . x-2<y-2
C . -2x<-2y
D .
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3.
将分式方程
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmfrac%3E%3Cmrow%3E%3Cmi%3Ex%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmfrac%3E%3C%2Fmath%3E)
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![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmfrac%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmi%3Ex%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmfrac%3E%3C%2Fmath%3E)
=3化为整式方程,正确的是( )
A . x-2=3
B . x+2=3
C . x-2=3(x-2)
D . x+2=3(x-2)
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4.
在△ABC中,点D , E是BC的三等分点,且△AED是等边三角形,则∠BAC的度数为( )
A . 100°
B . 110°
C . 120°
D . 130°
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5.
如图,将△
ABC绕点
C顺时针旋转,点
B的对应点为点
E , 点A的对应点为点
D,当点
E恰好落在边
AC上时,连接
AD , 若∠ACB=30°,则∠
DAC的度数是( )
![](//tikupic.21cnjy.com/2023/09/25/91/6f/916fb1c5ff934a7b127354c77c9f4ca9.png)
A . 60°
B . 65°
C . 70°
D . 75°
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6.
化简
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmfrac%3E%3Cmrow%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmi%3Ex%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmfrac%3E%3Cmo%3E%C3%B7%3C%2Fmo%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%3E4%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%3C%2Fmath%3E)
的结果为( )
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7.
如图,正比例函数
y=
kx(
k是常数,
k≠0)的图象与一次函数
y=-
x+6的图象相交于点
P , 则不等式-
x+6>
kx的解集是( )
![](//tikupic.21cnjy.com/2023/09/25/4b/a2/4ba2c839d4919e7fa742a5e0443083ea_225x215.png)
A . x>2
B . x<2
C . x>4
D . x<4
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8.
如图,在▱
ABCD中,对角线
AC , BD相交于点O,点
E ,
F分别是
AD , CD的中点,连接
OE、
OF , 若
OE=2,OF=3,则▱
ABCD 的周长为( )
![](//tikupic.21cnjy.com/2023/09/25/e7/65/e7656e7d2bd03259668ac4e80716d8db_205x115.png)
A . 10
B . 14
C . 16
D . 20
二、填空题(本大题共5个小题,每小题4分,共20分,答案写在答题卡上)</strong>
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10.
如果正n边形的一个内角与一个外角的比是2:1,则n的值为 .
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11.
若关于x的一元二次方程x2+2x-k=0无实数根,则k的取值范围是 .
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12.
如图,在平面直角坐标系
xOy中,线段
CD是由线段
AB平移得到的,B的坐标上,已知
A ,
C ,
D三点的坐标分别为(2,1),(4,2),(3,4),则点B的坐标为
.
![](//tikupic.21cnjy.com/2023/09/25/4b/ff/4bfffe87de1c295b327018ae1a8a4ddc_175x145.png)
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13.
如图,在△ABC中,AB=10,BC=6,AC=8,分别以点A,点B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%3EB%3C%2Fmi%3E%3C%2Fmath%3E)
的长为半径画弧,两弧相交于点M,N,作直线MN交AC于点D,则线段CD的长为
.
![](//tikupic.21cnjy.com/2023/09/25/86/6e/866ecd2319e22864531084e27861f72d_117x142.png)
三、解答题(本大题共5个小题,共48分,解答过程写在答题卡上)</strong>
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14.
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(1)
解不等式组:
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmo%3E%7B%3C%2Fmo%3E%3Cmtable+columnalign%3D%22left%22%3E%3Cmtr%3E%3Cmtd%3E%3Cmrow%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmn%3E4%3C%2Fmn%3E%3Cmo%3E%E2%89%A4%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%3Cmrow%3E%3Cmo%3E%28%3C%2Fmo%3E%3Cmrow%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmo%3E%29%3C%2Fmo%3E%3C%2Fmrow%3E%3C%2Fmrow%3E%3C%2Fmtd%3E%3C%2Fmtr%3E%3Cmtr%3E%3Cmtd%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmfrac%3E%3Cmrow%3E%3Cmn%3E3%3C%2Fmn%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmfrac%3E%3Cmo%3E%26lt%3B%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmtd%3E%3C%2Fmtr%3E%3C%2Fmtable%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
.
-
(2)
计算:
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmfrac%3E%3Cmrow%3E%3Cmsup%3E%3Cmrow%3E%3Cmi%3Em%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%3E4%3C%2Fmn%3E%3Cmi%3Em%3C%2Fmi%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmn%3E4%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmsup%3E%3Cmrow%3E%3Cmi%3Em%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%3C%2Fmfrac%3E%3Cmo%3E%C3%B7%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%3Cmrow%3E%3Cmi%3Em%3C%2Fmi%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmfrac%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmfrac%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmi%3Em%3C%2Fmi%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmfrac%3E%3C%2Fmath%3E)
.
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15.
如图,在平面直角坐标系
xOy中,已知△
ABC三个顶点的坐标分别为
A(1,1),
B(5,3),
C(3,4).
![](//tikupic.21cnjy.com/2023/09/25/29/15/291531543381487ce89751bf2b3fd4c7_270x273.png)
⑴画出△ABC关于原点O成中心对称的Δ A1B1C1;
⑵画出△ABC绕点O按逆时针方向旋转90°所得到的Δ A2B2C2;
⑶根据⑴(2)画出的图形,求出Δ AA1A2的面积.
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16.
在一次数学综合与实践活动中,同学们需要制作如图1所示的三种卡片,其中卡片①是边长为a的正方形:卡片②是长为b , 宽为a的长方形; 卡片③是边长为b的正方形
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(2)
小明制作了2张卡片①,3张卡片②,1张卡片③, 并用这些卡片无缝无叠合拼成如图2所示的长方形, 请根据图2的面积写一个多项式的因式分解为 ;
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(3)
小刚将自己制作的2张卡片①和1张卡片②送给小明,小明用所有卡片重新无缝无叠合拼成一个大的正方形
M , 若
a=1.6,b=2.8,求正方形
M的边长.
![](//tikupic.21cnjy.com/2023/09/25/54/3f/543fa3b1d4dde3a024d465df58f90c84_508x142.png)
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17.
如图,在▱
ABCD中,点
E , F在对角线AC上,且
AF=
CE , 连接
BE , DE,
BF ,
DF .
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(2)
若∠BAC=80°,AB=AF,DC=DF,求∠EBF的度数。
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18.
如图1,在△
ABC中,
AC=
BC , ∠ACB=120°,点
D是边
AB上一动点,将线段
CD绕点
C逆时针旋转120°得到CE,连接BE
.
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(2)
连接AE , 若AD=4,∠ACD=30°,求线段AE的长;
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(3)
如图2,若
AD=
AC ,
BD=2,点M为CD
中点,AM的延长线与
BC交于点
P , 与
BE交于点N,求线段BN的长。
四、填空题(本大题共3个小题,每小题3分,共9分,答案写在答题卡上)</strong>
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19.
已知x=y+3,则x2-2xy+y2的值为 .
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20.
已知不等式组
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmo%3E%7B%3C%2Fmo%3E%3Cmrow%3E%3Cmtable+columnalign%3D%22left%22%3E%3Cmtr+columnalign%3D%22left%22%3E%3Cmtd+columnalign%3D%22left%22%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmn%3E9%3C%2Fmn%3E%3Cmo%3E%E2%89%A4%3C%2Fmo%3E%3Cmn%3E4%3C%2Fmn%3E%3Cmi%3Ex%3C%2Fmi%3E%3C%2Fmtd%3E%3C%2Fmtr%3E%3Cmtr+columnalign%3D%22left%22%3E%3Cmtd+columnalign%3D%22left%22%3E%3Cmfrac%3E%3Cmrow%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmi%3Em%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmfrac%3E%3Cmo%3E%E2%89%A5%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmtd%3E%3C%2Fmtr%3E%3C%2Fmtable%3E%3C%2Fmrow%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
的解集为
x≥3,则
m的取值范围是
.
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21.
如图,在平行四边形
ABCD中,点
F是
AD上的点,AF=2DF,直线
BF交
AC于点
E ,
BE交
CD的延长线于点
G , 则
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmfrac%3E%3Cmrow%3E%3Cmi%3EB%3C%2Fmi%3E%3Cmi%3EE%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmi%3EE%3C%2Fmi%3E%3Cmi%3EG%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmfrac%3E%3C%2Fmath%3E)
.
![](//tikupic.21cnjy.com/2023/09/25/bb/88/bb8846701483e00889cd53af09357649_211x125.png)
五、解答题(11分)</strong>
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22.
在平行四边形
ABCD中,
AB=2,∠
ABC=45°,点
B的对应点为点
E , 线段
EC与边
AD交于点
F .
![](//tikupic.21cnjy.com/2023/09/25/de/7e/de7e4929365a1255d6dc147af30c7aaa.png)
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(2)
若△CDF是以CF为腰的等腰三角形,求线段BC的长;
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(3)
如图2,连接BE , CA的延长线交BE于点N , 当点M到BC的距离最小值时,求出此时△BCN的面积.