一、选择题(本题共10小题,每小题3分,共30分.每小题只有一个选项是正确的,不选、多选、错选,均不给分)
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2.
给定的三条线段中,不能组成三角形的是( )
A . 4,4,9
B . 3,5,6
C . 6,8,10
D . 5,12,13
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4.
若
![](//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%26lt%3B%3C%2Fmo%3E%3Cmi%3Ey%3C%2Fmi%3E%3C%2Fmath%3E)
, 则下列不等式成立的是( )
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5.
下列选项中,能说明命题“对于任何实数
![](//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)
, 都有
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmn%3E%7C%3C%2Fmn%3E%3Cmi%3Ea%3C%2Fmi%3E%3Cmn%3E%7C%3C%2Fmn%3E%3Cmo%3E%26gt%3B%3C%2Fmo%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmi%3Ea%3C%2Fmi%3E%3C%2Fmath%3E)
”是假命题的反例是( )
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6.
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%3Cmfrac%3E%3Cmrow%3E%3Cmi%3Ex%3C%2Fmi%3E%3C%2Fmrow%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%2Fmath%3E)
的自变量
![](//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)
的取值范围为( )
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7.
如图,两根竹竿AB和BD斜靠在墙上,量得
![](//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%3Cmi%3EA%3C%2Fmi%3E%3Cmi%3EB%3C%2Fmi%3E%3Cmn%3E++%EF%BC%8C+%3C%2Fmn%3E%3Cmo%3E%E2%88%A0%3C%2Fmo%3E%3Cmi%3EC%3C%2Fmi%3E%3Cmi%3ED%3C%2Fmi%3E%3Cmi%3EB%3C%2Fmi%3E%3C%2Fmath%3E)
的度数分别为
![](//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%3E8%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmo%3E%C2%B0%3C%2Fmo%3E%3C%2Fmrow%3E%3C%2Fmsup%3E%3C%2Fmath%3E)
和
![](//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%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)
, 那么
![](//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%3ED%3C%2Fmi%3E%3C%2Fmath%3E)
的度数为( )
![](//tikupic.21cnjy.com/2023/12/20/ad/b5/adb519ecca08bed84cf4039579567d01.png)
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8.
如图,
![](//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%3Cmi%3EA%3C%2Fmi%3E%3Cmi%3EB%3C%2Fmi%3E%3Cmo%3E%26lt%3B%3C%2Fmo%3E%3Cmi%3EA%3C%2Fmi%3E%3Cmi%3EC%3C%2Fmi%3E%3Cmo%3E%26lt%3B%3C%2Fmo%3E%3Cmi%3EB%3C%2Fmi%3E%3Cmi%3EC%3C%2Fmi%3E%3C%2Fmath%3E)
, 如果要使用尺规作图的方法在BC上确定一点
![](//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%3Cmi%3EP%3C%2Fmi%3E%3Cmi%3EA%3C%2Fmi%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmi%3EP%3C%2Fmi%3E%3Cmi%3EB%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3C%2Fmath%3E)
BC,那么符合要求的作图痕迹是( )
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9.
已知关于x的不等式
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmi%3Ea%3C%2Fmi%3E%3Cmtext%3E%E2%A9%BD%3C%2Fmtext%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmath%3E)
只有两个正整数解,则
![](//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)
的取值范围为( )
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10.
在图1所示的
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmn%3E3%3C%2Fmn%3E%3Cmo%3E%C3%97%3C%2Fmo%3E%3Cmn%3E3%3C%2Fmn%3E%3C%2Fmath%3E)
的网格内有一个八边形,其中每个小方格的边长均为1.经探究发现,此八边形可按图2的方式分割成四个全等的五边形和一个小正方形①.现将分割后的四个五边形重新拼接(即图2中的阴影部分),得到一个大正方形ABCD,发现该正方形中间的空白部分②也是个正方形,记正方形①得面积为S
1 , 正方形②的面积为S
2 , 且
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3ES%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3Cmn%3E%EF%BC%9A%3C%2Fmn%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3ES%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%3Cmn%3E3%3C%2Fmn%3E%3Cmn%3E%EF%BC%9A%3C%2Fmn%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmath%3E)
, 则大正方形ABCD的边长为( )
![](//tikupic.21cnjy.com/2024/01/18/cf/fe/cffe8760936d710b92b2feb117e653d8_435x241.png)
二、填空题(本题共8小题,每小题3分,共24分)
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11.
用不等式表示“
![](//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)
的2倍与1的和是正数”:
.
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13.
在平面直角坐标系中,点
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmn%3E%28%3C%2Fmn%3E%3Cmn%3E3%3C%2Fmn%3E%3Cmn%3E++%EF%BC%8C+%3C%2Fmn%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmn%3E5%3C%2Fmn%3E%3Cmn%3E%29%3C%2Fmn%3E%3C%2Fmath%3E)
到
![](//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)
轴的距离是
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14.
如图是在固定的电压下,一电阻的阻值
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3ER%3C%2Fmi%3E%3Cmn%3E%28%3C%2Fmn%3E%3Cmtext%3E%CE%A9%3C%2Fmtext%3E%3Cmn%3E%29%3C%2Fmn%3E%3C%2Fmath%3E)
与通过该电阻的电流
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EI%3C%2Fmi%3E%3Cmn%3E%28%3C%2Fmn%3E%3Cmtext%3EA%3C%2Fmtext%3E%3Cmn%3E%29%3C%2Fmn%3E%3C%2Fmath%3E)
之间的函数关系图.根据图象,当自变量
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EI%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmn%3E%28%3C%2Fmn%3E%3Cmtext%3EA%3C%2Fmtext%3E%3Cmn%3E%29%3C%2Fmn%3E%3C%2Fmath%3E)
时,函数值为
.
![](//tikupic.21cnjy.com/2024/01/18/20/48/2048fb5d49924cf13f4e64d9bf48599c_220x220.png)
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15.
某业主贷款22000元购进一台机器,生产某种产品.已知产品的成本每个5元,售价是每个8元.若每月能生产、销售2000个产品,问至少个月后能赚回这台机器的贷款.
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16.
如图,在平面直角坐标系中,直线
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3El%3C%2Fmi%3E%3C%2Fmath%3E)
是一、三象限的角平分线,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)
是直线
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3El%3C%2Fmi%3E%3C%2Fmath%3E)
上的一个动点,
![](//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%3Cmn%3E3%3C%2Fmn%3E%3Cmn%3E++%EF%BC%8C+%3C%2Fmn%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmn%3E%29%3C%2Fmn%3E%3Cmn%3E++%EF%BC%8C+%3C%2Fmn%3E%3Cmi%3EB%3C%2Fmi%3E%3Cmn%3E%28%3C%2Fmn%3E%3Cmn%3E6%3C%2Fmn%3E%3Cmn%3E++%EF%BC%8C+%3C%2Fmn%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmn%3E%29%3C%2Fmn%3E%3C%2Fmath%3E)
是
![](//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)
轴上的两个点,则
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EP%3C%2Fmi%3E%3Cmi%3EA%3C%2Fmi%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmi%3EP%3C%2Fmi%3E%3Cmi%3EB%3C%2Fmi%3E%3C%2Fmath%3E)
的最小值为
.
![](//tikupic.21cnjy.com/2024/01/18/78/fd/78fd7afa32982c01a1268ed7477b90da_168x136.png)
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17.
如图,
![](//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%3EO%3C%2Fmi%3E%3Cmi%3EB%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)
, 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%3Cmo%3E%E2%88%A0%3C%2Fmo%3E%3Cmi%3EA%3C%2Fmi%3E%3Cmi%3EO%3C%2Fmi%3E%3Cmi%3EB%3C%2Fmi%3E%3C%2Fmath%3E)
平分线OC上一点,OD的垂直平分线交OA,OB分别于点P,Q,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OA上异于点
![](//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)
的一点,且
![](//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%3EE%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmi%3EO%3C%2Fmi%3E%3Cmi%3EP%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmath%3E)
, 则
![](//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%3EO%3C%2Fmi%3E%3Cmi%3ED%3C%2Fmi%3E%3Cmi%3EE%3C%2Fmi%3E%3C%2Fmath%3E)
的面积为
.
![](//tikupic.21cnjy.com/2024/01/18/5b/e0/5be0331137de436f31eaa584287fdfa6_228x138.png)
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18.
如图是一个提供床底收纳支持的气压伸缩杆,除了AB是完全固定的钢架外,AD,BC,DE属于位置可变的定长钢架.如图1所示,
![](//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%3EB%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmn%3E9%3C%2Fmn%3E%3Cmtext%3Ec%3C%2Fmtext%3E%3Cmtext%3Em%3C%2Fmtext%3E%3Cmn%3E++%EF%BC%8C+%3C%2Fmn%3E%3Cmi%3EA%3C%2Fmi%3E%3Cmi%3ED%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmn%3E3%3C%2Fmn%3E%3Cmtext%3Ec%3C%2Fmtext%3E%3Cmtext%3Em%3C%2Fmtext%3E%3Cmn%3E++%EF%BC%8C+%3C%2Fmn%3E%3Cmi%3EB%3C%2Fmi%3E%3Cmi%3EC%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmtext%3Ec%3C%2Fmtext%3E%3Cmtext%3Em%3C%2Fmtext%3E%3C%2Fmath%3E)
, 伸缩杆PQ的两端分别固定在BC,CE两边上,其中
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EP%3C%2Fmi%3E%3Cmi%3EB%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmn%3E3%3C%2Fmn%3E%3Cmtext%3Ec%3C%2Fmtext%3E%3Cmtext%3Em%3C%2Fmtext%3E%3Cmn%3E++%EF%BC%8C+%3C%2Fmn%3E%3Cmi%3EC%3C%2Fmi%3E%3Cmi%3EQ%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmtext%3Ec%3C%2Fmtext%3E%3Cmtext%3Em%3C%2Fmtext%3E%3C%2Fmath%3E)
.当伸缩杆PQ打开最大时,如图2所示,
![](//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%3ED%3C%2Fmi%3E%3Cmi%3EC%3C%2Fmi%3E%3C%2Fmath%3E)
成
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmn%3E8%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)
, 此时
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EP%3C%2Fmi%3E%3Cmi%3EQ%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmsqrt%3E%3Cmrow%3E%3Cmn%3E4%3C%2Fmn%3E%3Cmn%3E4%3C%2Fmn%3E%3Cmn%3E9%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsqrt%3E%3Cmtext%3Ec%3C%2Fmtext%3E%3Cmtext%3Em%3C%2Fmtext%3E%3C%2Fmath%3E)
, 则可变定长钢架CD的长度为
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmtext%3Ec%3C%2Fmtext%3E%3Cmtext%3Em%3C%2Fmtext%3E%3C%2Fmath%3E)
.当伸缩杆完全收拢时,
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EC%3C%2Fmi%3E%3Cmi%3ED%3C%2Fmi%3E%3Cmn%3E%2F%3C%2Fmn%3E%3Cmn%3E%2F%3C%2Fmn%3E%3Cmi%3EA%3C%2Fmi%3E%3Cmi%3EB%3C%2Fmi%3E%3C%2Fmath%3E)
, 则此时床高(CD与AB之间的距离)为
cm.
![](//tikupic.21cnjy.com/2024/01/18/d2/6f/d26feb7d72643d58f1c9db1b1d0f1cc0_484x198.png)
三、解答题(本题有6小题,共46分)
-
19.
解下列不等式(组).
-
-
(2)
-
20.
如图,已知AB=DC,AC=DB.求证:∠A=∠D.
下面是两位同学的对话:
方方说:根据条件,找不到全等三角形.
圆圆说:如果添加辅助线,就可以找到全等三角形了.
请根据提示给出证明.
![](//tikupic.21cnjy.com/2023/11/24/ba/2c/ba2c831de7eca19ae941d683bdb6d696_m_201x147.png)
-
21.
如图所示,在平面直角坐标系中,点
![](//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)
为坐标原点,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)
的坐标为
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmn%3E%28%3C%2Fmn%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmn%3E++%EF%BC%8C+%3C%2Fmn%3E%3Cmn%3E3%3C%2Fmn%3E%3Cmn%3E%29%3C%2Fmn%3E%3C%2Fmath%3E)
.
![](//tikupic.21cnjy.com/2024/01/18/f8/e3/f8e38160372b206c5a7d96f21d62afba_370x369.png)
-
(1)
将点
![](//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)
向右平移1个单位,向下平移2个单位所得的点
![](//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)
的坐标为
;
-
-
(3)
在平面直角坐标系中标出点B,C所在位置,并求出四边形OBAC的面积.
-
22.
在△ABC中,
![](//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%3EB%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmi%3EA%3C%2Fmi%3E%3Cmi%3EC%3C%2Fmi%3E%3Cmn%3E++%EF%BC%8C+%3C%2Fmn%3E%3Cmi%3EA%3C%2Fmi%3E%3Cmi%3ED%3C%2Fmi%3E%3Cmo%3E%E2%8A%A5%3C%2Fmo%3E%3Cmi%3EB%3C%2Fmi%3E%3Cmi%3EC%3C%2Fmi%3E%3Cmn%3E++%EF%BC%8C+%3C%2Fmn%3E%3Cmi%3EE%3C%2Fmi%3E%3C%2Fmath%3E)
为AC边上一点,过点
![](//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)
作
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EB%3C%2Fmi%3E%3Cmi%3EF%3C%2Fmi%3E%3Cmn%3E%2F%3C%2Fmn%3E%3Cmn%3E%2F%3C%2Fmn%3E%3Cmi%3EA%3C%2Fmi%3E%3Cmi%3EC%3C%2Fmi%3E%3C%2Fmath%3E)
交ED延长线于点
![](//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)
.
![](//tikupic.21cnjy.com/2024/01/18/b5/b1/b5b1ffdbc1389707f7b77304e9715420_231x165.png)
-
(1)
求证:
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EB%3C%2Fmi%3E%3Cmi%3EF%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmi%3EC%3C%2Fmi%3E%3Cmi%3EE%3C%2Fmi%3E%3C%2Fmath%3E)
.
-
(2)
连结BE,若
![](//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AC中点,
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EB%3C%2Fmi%3E%3Cmi%3EF%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E5%3C%2Fmn%3E%3Cmn%3E++%EF%BC%8C+%3C%2Fmn%3E%3Cmi%3EA%3C%2Fmi%3E%3Cmi%3ED%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E6%3C%2Fmn%3E%3C%2Fmath%3E)
, 求BE的长.
-
23.
某中学计划购买A型和
![](//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)
型课桌凳共200套,经招标,购买一套
![](//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)
型课桌凳比购买一套
![](//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)
型课桌凳少用40元,且购买3套
![](//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)
型和5套
![](//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)
型课桌凳共需1640元.
-
(1)
求购买一套
![](//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)
型课桌凳和一套
![](//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)
型课桌凳各需多少元?
-
(2)
学校根据实际情况,要求购买这两种课桌凳的总费用不能超过40880元,并且购买
![](//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)
型课桌凳的数量不能超过
![](//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)
型课桌凳数量的
![](//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%3E3%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmfrac%3E%3C%2Fmath%3E)
, 求该校本次购买
![](//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)
型和
![](//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)
型课桌凳共有几种购买方案?怎样的方案使总费用最低?并求出最低消费.
-
24.
如图1,在平面直角坐标系中,
![](//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)
点坐标为
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmn%3E%28%3C%2Fmn%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmn%3E++%EF%BC%8C+%3C%2Fmn%3E%3Cmn%3E4%3C%2Fmn%3E%3Cmn%3E%29%3C%2Fmn%3E%3Cmn%3E++%EF%BC%8C+%3C%2Fmn%3E%3Cmi%3EB%3C%2Fmi%3E%3C%2Fmath%3E)
点坐标为
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmn%3E%28%3C%2Fmn%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmn%3E++%EF%BC%8C+%3C%2Fmn%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmn%3E%29%3C%2Fmn%3E%3Cmn%3E++%EF%BC%8C+%3C%2Fmn%3E%3Cmi%3EC%3C%2Fmi%3E%3C%2Fmath%3E)
是
![](//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)
轴负半轴上一点,且
![](//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%3EB%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmi%3EA%3C%2Fmi%3E%3Cmi%3EC%3C%2Fmi%3E%3Cmn%3E++%EF%BC%8C+%3C%2Fmn%3E%3Cmi%3EP%3C%2Fmi%3E%3C%2Fmath%3E)
是
![](//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)
轴正半轴上一点,作
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EP%3C%2Fmi%3E%3Cmi%3ED%3C%2Fmi%3E%3Cmo%3E%E2%8A%A5%3C%2Fmo%3E%3Cmi%3EB%3C%2Fmi%3E%3Cmi%3EC%3C%2Fmi%3E%3C%2Fmath%3E)
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)
, 连接OD.
![](//tikupic.21cnjy.com/2024/01/18/a0/0a/a00a84f1f03a5a665cea7f152bf64d05_389x274.png)
-
(1)
C点坐标为
,
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EB%3C%2Fmi%3E%3Cmi%3EC%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3C%2Fmath%3E)
.
-
(2)
①当点
![](//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)
在线段OA上时,若
![](//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%3EO%3C%2Fmi%3E%3Cmi%3EB%3C%2Fmi%3E%3Cmi%3ED%3C%2Fmi%3E%3C%2Fmath%3E)
是以OB为腰的等腰三角形,请求出所有符合条件的
![](//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)
点坐标.
②如图2,设DP交直线AC于点
, 连结CP,若
, 则
(直接写出结果).