一、<table border=0 cellspacing=0 cellpadding=0 > <tr > <td > <p><b >单选题</b></p> </td> </tr> </table>
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1.
若|1﹣x|=1+|x|,则
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmsqrt%3E%3Cmrow%3E%3Cmsup%3E%3Cmrow%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%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmsup%3E%3C%2Fmrow%3E%3C%2Fmsqrt%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
等于( ).
A . x﹣1
B . 1﹣x
C . 1
D . ﹣1
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2.
设0<k<1,关于x的一次函数y=kx+
![](//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%3Cmi%3Ek%3C%2Fmi%3E%3C%2Fmfrac%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
(1﹣x),当1≤x≤2时,y的最大值是( ).
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3.
如图,O是△ABC的外心,OD⊥BC,OE⊥AC,OF⊥AB,则OD:OE:OF等于( ).
![](//tikupic.21cnjy.com/30/e6/30e6461fcb8f535aa6c6f27e15018d61.png)
A . a:b:c
B .
C . sinA:sinB:sinC
D . cosA:cosB:cosC
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4.
正方形ABCD、正方形BEFG和正方形DMNK的位置如图所示,点A在线段NF上,AE=8,则△NFP的面积为( ).
![](//tikupic.21cnjy.com/78/fa/78fa1f5d10f45ca3c1441169db9cd848.png)
A . 30
B . 32
C . 34
D . 36
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二、<table border=0 cellspacing=0 cellpadding=0 > <tr > <td > <p><b >填空题</b></p> </td> </tr> </table>
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6.
如果实数x、y满足2x
2﹣6xy+9y
2﹣4x+4=0,那么
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmroot%3E%3Cmi%3Ey%3C%2Fmi%3E%3Cmi%3Ex%3C%2Fmi%3E%3C%2Fmroot%3E%3C%2Fmath%3E)
=
.
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7.
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%3Cmfrac%3E%3Cmi%3Ea%3C%2Fmi%3E%3Cmrow%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmfrac%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
=1的解是负数,则a的取值范围是
.
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8.
如图,⊙O中,BD为⊙O直径,弦AD长为3,AB长为5,AC平分∠DAB,则弦AC的长为
.
![](//tikupic.21cnjy.com/a1/26/a1264eb369a73f6ad471d22ee0c5fb82.png)
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9.
在平面直角坐标系中,A(2,0)、B(0,3),过点B作直线∥x轴,点P(a,3)是直线上的动点,以AP为边在AP右侧作等腰RtAPQ,∠APQ=90°,直线AQ交y轴于点C.
![](//tikupic.21cnjy.com/e1/ce/e1ce395699cd94d2c480bdc65e3ad69a.png)
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(2)
当点P在直线上运动时,点Q也随之运动.当a=时,AQ+BQ的值最小为.
三、<table border=0 cellspacing=0 cellpadding=0 > <tr > <td > <p><b >解答题</b></p> </td> </tr> </table>
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10.
如图,等腰△ABC中,AC=BC,⊙O为△ABC的外接圆,D为
![](//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%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)
上一点,CE⊥AD于E,求证:AE=BD+DE.
![](//tikupic.21cnjy.com/d1/50/d1502b5df15a654ed9344716a623d246.png)
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11.
如图,已知抛物线y=
![](//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)
x
2+mx+n(n≠0)与直线y=x交于A、B两点,与y轴交于点C,OA=OB,BC∥x轴.
![](//tikupic.21cnjy.com/bd/8f/bd8f65432d0a498285ffd410c47f0ef4.png)
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(2)
设D、E是线段AB上异于A、B的两个动点(点E在点D的上方),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%3E2%3C%2Fmn%3E%3C%2Fmsqrt%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
,过D、E两点分别作y轴的平行线,交抛物线于F、G,若设D点的横坐标为x,四边形DEGF的面积为y,求x与y之间的关系式,写出自变量x的取值范围,并回答x为何值时,y有最大值.