一、选择题:本大题有10个小题,每小题3分,共30分.在每小题给出的四个选项中,只有一项是符合题目要求的.
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A . ﹣6
B . 6
C . ﹣8
D . 8
-
2.
如图,某人从
A地出发,沿正东方向前进至
B处后右转30°,则他应( )
![](//tikupic.21cnjy.com/2024/05/08/66/1f/661f36978ca198b16f7e02fb51322f99.png)
A . 先右转30°,再直行
B . 先右转150°,再直行
C . 先左转30°,再直行
D . 先左转150°,再直行
-
3.
已知数据
x1 ,
x2…,
x10的方差计算公式为
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsup%3E%3Cmrow%3E%3Cmi%3ES%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsup%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmfrac%3E%3Cmrow%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E10%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmfrac%3E%3Cmfenced+open%3D%22%5B%22+close%3D%22%5D%22%3E%3Cmrow%3E%3Cmsup%3E%3Cmrow%3E%3Cmfenced%3E%3Cmrow%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3Ex%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmn%3E4%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmfenced%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsup%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmsup%3E%3Cmrow%3E%3Cmfenced%3E%3Cmrow%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3Ex%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmn%3E4%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmfenced%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsup%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmo%3E%E2%8B%AF%3C%2Fmo%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmsup%3E%3Cmrow%3E%3Cmfenced%3E%3Cmrow%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3Ex%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E10%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmn%3E4%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmfenced%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsup%3E%3C%2Fmrow%3E%3C%2Fmfenced%3E%3C%2Fmath%3E)
, 则这组数据的( )
A . 方差为40
B . 中位数为4
C . 平均数为4
D . 标准差为40
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4.
已知a是有理数,b是无理数,下列算式的结果必定为无理数的是( )
A . a+b
B . ab
C .
D .
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5.
如图,中国古代用算筹记数,有纵式和横式两种.算筹记数的方法是摆个位为纵,百位为纵,千位为横…这样纵横依次交替,数位从高到低.如257表示为
![](//tikupic.21cnjy.com/2024/05/08/f5/e2/f5e2721fe83cddbf7ca8c0dec69084ac.png)
, 则3182可表示为( )
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6.
如图,在等边三角形
ABC中,点
D ,
AC边上,点
D不与点
B , 且
BD=
CE , 则( )
![](//tikupic.21cnjy.com/2024/05/08/45/ac/45ac9b2260eba6d2b1b7924f54ccfedf.png)
A . ∠AFE<∠FAE
B . ∠AFE<∠FEA
C . ∠AFE=∠FAE
D . ∠AFE=∠FEA
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7.
在△ABC中,已知∠C=90°,设q=sinA+cosA , 则( )
A . q<1
B . q≤1
C . q=1
D . q>1
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8.
如图,在△ABC中,已知
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi+mathvariant%3D%22normal%22%3EB%3C%2Fmi%3E%3Cmi+mathvariant%3D%22normal%22%3EC%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E4%3C%2Fmn%3E%3Cmsqrt%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmsqrt%3E%3Cmo%3E%2C%3C%2Fmo%3E%3Cmi+mathvariant%3D%22normal%22%3Ec%3C%2Fmi%3E%3Cmi+mathvariant%3D%22normal%22%3Eo%3C%2Fmi%3E%3Cmi+mathvariant%3D%22normal%22%3Es%3C%2Fmi%3E%3Cmo%3E%E2%81%A1%3C%2Fmo%3E%3Cmi+mathvariant%3D%22normal%22%3EA%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmfrac%3E%3Cmrow%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E3%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmfrac%3E%3C%2Fmath%3E)
,O是△ABC的外心,D是BC的中点,则OD= ( )
![](//tikupic.21cnjy.com/2024/05/08/ba/45/ba45b6867b9d394704075ecd31beb818.png)
A . 2
B .
C . 1
D .
-
9.
如图,已知E是正方形ABCD内一点,设∠EBC=α,∠EDC=β,∠BAE=γ,∠DAE=θ,若AE=AB,则( )
![](//tikupic.21cnjy.com/2024/05/08/5e/fd/5efdfe437a134dfeb5ee188d4d4ee3fe.png)
A .
B .
C . α+θ=β+γ
D . 2(α+γ)=θ+β
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10.
已知ac≠0,若二次函数y1=ax2+bx+c的图象与x轴交于两个不同的点A(x1 , 0),B(x2 , 0),二次函数y2=cx2+bx+a的图象与x轴交于两个不同的点C(x3 , 0),D(x4 , 0),则( )
A . x1+x2+x3+x4=1
B . x1x2x3x4=1
C .
D .
二、填空题:本大题有6个小题,每小题3分,共18分.
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-
-
13.
在一个木盒中有2个红球和2个黄球(这些球除了颜色,其余均相同),从中随意取出2个球,则恰好这2个球的颜色相同的概率是 .
-
14.
如图,在△ABC中,已知AC=4,BC=3,D是AB上一点,连接CD.若AD=2DB,且△BCD∽△BAC,则CD的长为
.
![](//tikupic.21cnjy.com/2024/05/08/e5/08/e508ef835e805a9fa078a49b4ca118d6.png)
-
15.
已知
A(
x1 ,
y1),
B(
x2 ,
y2)是一次函数
y=2
x﹣3图象上两个不同的点,则
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmfrac%3E%3Cmrow%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3Ey%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3Ey%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3Ex%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3Ex%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3C%2Fmrow%3E%3C%2Fmfrac%3E%3C%2Fmath%3E)
=
.
-
16.
图,在正方形ABCD中,G为BC上一点,矩形DEFG的边EF经过点A.若∠CDG=α,则∠AHF=
;若
AH=3,
GC=2,则△
EFH的面积为
.
![](//tikupic.21cnjy.com/2024/05/08/99/49/9949bb657206098dcb69de4da45c20e5.png)
三、解答题:本大题有8个小题,共72分.解答应写出文字说明、证明过程或演算步骤.
-
17.
如图,
AC是菱形
ABCD的一条对角线,点
B在射线
AE上.
![](//tikupic.21cnjy.com/2024/05/08/33/e4/33e45df0b4656a04f2b531d1b9b5021e.png)
-
(1)
请用尺规把这个菱形补充完整.(保留作图痕迹,不要求写作法)
-
(2)
若
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi+mathvariant%3D%22normal%22%3EA%3C%2Fmi%3E%3Cmi+mathvariant%3D%22normal%22%3EC%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E6%3C%2Fmn%3E%3Cmsqrt%3E%3Cmn%3E3%3C%2Fmn%3E%3C%2Fmsqrt%3E%3Cmo%3E%2C%3C%2Fmo%3E%3Cmi+mathvariant%3D%22normal%22%3E%E2%88%A0%3C%2Fmi%3E%3Cmi%3EC%3C%2Fmi%3E%3Cmi%3EA%3C%2Fmi%3E%3Cmi%3EB%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmsup%3E%3Cmrow%3E%3Cmn%3E30%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmo%3E%E2%88%98%3C%2Fmo%3E%3C%2Fmrow%3E%3C%2Fmsup%3E%3C%2Fmath%3E)
, 求菱形
ABCD的面积.
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18.
在一次数学综合实践活动中,需要制作如图所示的零件(长方体和圆锥的组合体),为此方方同学画出了该零件的三视图.
![](//tikupic.21cnjy.com/2024/05/08/15/28/1528dad40e0f09cb206517ffcaf062fb.png)
-
(1)
请问方方所画的三个视图是否有错?如有错,请将错的视图改正.
-
(2)
根据图中尺寸,求出其体积.(注:长方体的底面为正方形,单位:cm , 结果保留一位小数)
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19.
如图,函数
y1=
x与
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsub%3E%3Cmrow%3E%3Cmi+mathvariant%3D%22normal%22%3Ey%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%3Cmfrac%3E%3Cmrow%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmi+mathvariant%3D%22normal%22%3Ex%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmfrac%3E%3C%2Fmath%3E)
的图象交于
A ,
B两点.
![](//tikupic.21cnjy.com/2024/05/08/28/85/2885c214707703b58074211662d40aa7.png)
-
-
(2)
借助图象信息,解不等式
![](//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%3Cmfrac%3E%3Cmrow%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmi%3Ex%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmfrac%3E%3C%2Fmath%3E)
.
-
20.
为了考察甲、乙两种小麦的长势,分别从中随机抽取10株麦苗,测得苗高(单位:
cm)
甲 | 12 | 13 | 14 | 15 | 10 | 16 | 13 | 11 | 15 | 11 |
乙 | 11 | 16 | 17 | 14 | 13 | 19 | 6 | 8 | 10 | 16 |
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-
-
21.
如图,点
B在以
DE为直径的半圆上,
A为圆心,连接
AB , 设
DC=
m , 且
m>
n .
![](//tikupic.21cnjy.com/2024/05/08/13/33/1333f57931912388e2b676bbf8c26475.png)
-
(1)
请用m , n表示Rt△ABC的三条边长.
-
(2)
若m , n均为不超过20的正整数,且使Rt△ABC的三条边长都是整数,n的值.
-
22.
已知函数
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3Ey%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmi%3Em%3C%2Fmi%3E%3Cmsup%3E%3Cmrow%3E%3Cmi+mathvariant%3D%22normal%22%3Ex%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsup%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmi%3En%3C%2Fmi%3E%3Cmo%3E%2C%3C%2Fmo%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3Ey%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%3Cmi%3Em%3C%2Fmi%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmi%3En%3C%2Fmi%3E%3Cmo%3E%28%3C%2Fmo%3E%3Cmi%3Em%3C%2Fmi%3E%3Cmo%3E%26gt%3B%3C%2Fmo%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmo%3E%29%3C%2Fmo%3E%3C%2Fmath%3E)
的图象在同一平面直角坐标系中.
-
(1)
若函数y1的图象过点(﹣2,6),函数y2的图象过点(t , 6),求t的值.
-
-
(3)
已知当p<x<q时,y1<y2 , 求q﹣p的取值范围.
-
23.
如图,
AB和
BC分别是⊙
O1的直径和弦,⊙
O2与⊙
O1关于
BC轴对称,⊙
O2交
AB于点
D ,
O1O2交
BC于点
E .
![](//tikupic.21cnjy.com/2024/05/08/67/6a/676af2a99d90df333aa0f5965cd32dab.png)
-
-
-
-
24.
设一次函数
y1=
a(
x+
m)的图象与
x轴交于点
A , 二次函数
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3Ey%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%3Cmi%3Ea%3C%2Fmi%3E%3Cmsup%3E%3Cmrow%3E%3Cmi%3Ex%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsup%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmi%3Eb%3C%2Fmi%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmi%3Ec%3C%2Fmi%3E%3C%2Fmath%3E)
的图象与x轴交于A,B两个不同的点,设函数y=y
1+y
2 .
-
(1)
设点Q(0,q)在函数y的图象上,若q>c,求证:am>0.
-
(2)
若函数y2 , y的图象在x轴上截得的线段长分别为d1 , d2 , 求d1 , d2的数量关系式.
-
(3)
若函数y1的图象分别与函数y2的图象、函数y的图象交于点E(x1 , e),F(x2 , f),且点E,F不同于点A,求x1-x2的值.