全一卷
1.
等于( )
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A.![]() | B.![]() | C.![]() | D.![]() |
2.在
,
,
,
这四个数中,绝对值最小的数是( )
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A.![]() | B.![]() | C.![]() | D.![]() |
3.用四舍五入法将
精确到千位,正确的是( )
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A.![]() | B.![]() | C.![]() | D.![]() |
4.下列运算正确的是( )
A.![]() | B.![]() |
C.![]() | D.![]() |
5.如图,
∥
,
,
,则
的度数是( )
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A.![]() | B.![]() |
C.![]() | D.![]() |
6.下列说法错误的是( )
A.平行四边形的对边相等 | B.对角线相等的四边形是矩形 |
C.对角线互相垂直的平行四边形是菱形 | D.正方形既是轴对称图形、又是中心对称图形 |
7.比较A组、B组中两组数据的平均数及方差,一下说法正确的是( )
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A.A组,B组平均数及方差分别相等 | B.A组,B组平均数相等,B组方差大 |
C.A组比B组的平均数、方差都大 | D.A组,B组平均数相等,A组方差大 |
8.一辆货车送上山,并按原路下山.上山速度为
千米/时,下山速度为
千米/时.则货车上、下山的平均速度为( )千米/时.
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A.![]() | B.![]() | C.![]() | D.![]() |
9.在同一坐标系中,二次函数
与一次函数
的图像可能是( )
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A.![]() | B.![]() |
C.![]() | D.![]() |
10.
的相反数是__________
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11.分解因式:
__________
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12.一组数据1,2,
,5,8的平均数是5,则该组数据的中位数是____________
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13.已知
、
是方程
的两根,则
______________
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14.如图是一个多面体的表面展开图,如果面
在前面,从左面看是面
(字母面在外面),那么从上面看是面__________ (填字母)
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15.正方形
,
,
,…按如图所示的方式放置,点
,
,
,…和点
,
,
,…分别在直线
(
)和
轴上.已知
,点
,则
的坐标是_____________
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16.解不等式,并把它的解集在数轴上表示出来.
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17.如图,在
中,
是
边上的高,
是
边上的中线,且
求证:(1)点
在
的垂直平分线上;(2)
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求证:(1)点
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18.某市少年宫为小学生开设了绘画、音乐、舞蹈和跆拳道四类兴趣班,为了解学生对这四类兴趣班的喜爱情况,对学生进行了随机问卷调查(问卷调查表如图所示),将调查结果整理后绘制了一幅不完整的统计表
请你根据统计表中提供的信息回答下列问题:
(1)统计表中的
,
;
(2)根据调查结果,请你估计该市2000名小学生中最喜欢“绘画”兴趣的人数;
(3)王姝和李要选择参加兴趣班,若他们每人从
、
、
、
四类兴趣班中随机选取一类,请用画树状图或列表格的方法,求两人恰好选中同一类的概率.
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兴趣班 | 频数 | 频率 |
A |
| 0.35 |
B | 18 | 0.30 |
C | 15 | |
D | 6 |
|
合计 | 1 |
(1)统计表中的
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(2)根据调查结果,请你估计该市2000名小学生中最喜欢“绘画”兴趣的人数;
(3)王姝和李要选择参加兴趣班,若他们每人从
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19.如图,在平面直角坐标系
中,一次函数
的图像与反比例函数
的图像在第二象限交于点
,与
轴交于点
,点
在
轴上,满足条件:
,且
,点
的坐标为
,
。
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(1)求反比例函数的表达式;
(2)直接写出当
时,
的解集。
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(1)求反比例函数的表达式;
(2)直接写出当
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20.攀枝花得天独厚,气候宜人,农产品资源极为丰富,其中晚熟芒果远销北上广等大城市.某水果店购进一批优质晚熟芒果,进价为10元/千克,售价不低于15元/千克,且不超过40元/每千克,根据销售情况,发现该芒果在一天内的销售量
(千克)与该天的售价
(元/千克)之间的数量满足如下表所示的一次函数关系.
(1)某天这种芒果售价为28元/千克.求当天该芒果的销售量
(2)设某天销售这种芒果获利
元,写出
与售价
之间的函数关系式.如果水果店该天获利400元,那么这天芒果的售价为多少元?
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销售量 | … | 32.5 | 35 | 35.5 | 38 | … |
售价 | … | 27.5 | 25 | 24.5 | 22 | … |
(2)设某天销售这种芒果获利
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21.如图1,有一个残缺的圆,请做出残缺圆的圆心
(保留作图痕迹,不写做法)
如图2,设
是该残缺圆
的直径,
是圆上一点,
的角平分线
交
于点
,过点
作
的切线交
的延长线于点
.
(1)求证:
;(2)若
,
,求残缺圆的半圆面积.
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如图2,设
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(1)求证:
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22.已知抛物线
的对称轴为直线
,其图像与
轴相交于
、
两点,与
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(1)求
,
的值;
(2)直线
与
轴交于点
.
①如图1,若
∥
轴,且与线段
及抛物线分别相交于点
、
,点
关于直线
的对称点为
,求四边形
面积的最大值;
②如图2,若直线
与线段
相交于点
,当
∽
时,求直线
的表达式.
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(1)求
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(2)直线
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①如图1,若
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②如图2,若直线
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23.在平面直角坐标系
中,已知
,动点
在
的图像上运动(不与
重合),连接
,过点
作
,交
轴于点
,连接
.
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(1)求线段
长度的取值范围;
(2)试问:点
运动过程中,
是否问定值?如果是,求出该值;如果不是,请说明理由.
(3)当
为等腰三角形时,求点
的坐标.
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(1)求线段
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(2)试问:点
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(3)当
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